All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek Die Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliograﬁe; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de. # 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microﬁlm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not speciﬁcally marked as such, are not to be considered unprotected by law. Composition Thomson Digital, Noida, India Printing betz-druck GmbH, Darmstadt Binding Litges & Dopf GmbH, Heppenheim Cover Design Adam-Design, Weinheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-31557-4

Series Preface The present series is dedicated to drying, i.e. to the process of removing moisture from solids. Drying has been conducted empirically since the dawn of the human race. In traditional scientiﬁc terms it is a unit operation in chemical engineering. The reason for the continuing interest in drying and, hence, the motivation for the series concerns the challenges and opportunities. A permanent challenge is connected to the sheer amount and value of products that must be dried – either to attain their functionalities, or because moisture would damage the material during subsequent processing and storage, or simply because customers are not willing to pay for water. This comprises almost every material used in solid form, from foods to pharmaceuticals, from minerals to detergents, from polymers to paper. Raw materials and commodities with a low price per kilogram, but with extremely high production rates, and also highly formulated, rather rare but very expensive specialties have to be dried. This permanent demand is accompanied by the challenge of sustainable development providing welfare, or at least a decent living standard, to a stillgrowing humanity. On the other hand, opportunities emerge for drying, as well as for any other aspect of science or living, from either the incremental or disruptive development of available tools. This duality is reﬂected in the structure of the book series, which is planned for ﬁve volumes in total, namely: Volume 1: Computational tools at different scales Volume 2: Experimental techniques Volume 3: Product quality and formulation Volume 4: Energy savings Volume 5: Process intensiﬁcation As the titles indicate, we start with the opportunities in terms of modern computational and experimental tools in Volumes 1 and 2, respectively. How these opportunities can be used in fulﬁlling the challenges, in creating better and new products, in reducing the consumption of energy, in signiﬁcantly improving existing or introducing new processes will be discussed in Volumes 3, 4 and 5. In this sense, the ﬁrst two volumes of the series will be driven by science; the last three will try to show how engineering science and technology can be translated into progress.

In total, the series is designed to have both common aspects with and essential differences from an extended textbook or a handbook. Textbooks and handbooks usually refer to well-established knowledge, prepared and organized either for learning or for application in practice, respectively. On the contrary, the ambition of the present series is to move at the frontier of modern drying technology, describing things that have recently emerged, mapping things that are about to emerge, and also anticipating some things that may or should emerge in the near future. Consequently, the series is much closer to research than textbooks or handbooks can be. On the other hand, it was never intended as an anthology of research papers or keynotes – this segment being well covered by periodicals and conference proceedings. Therefore, our continuing effort will be to stay as close as possible to a textbook in terms of understandable presentation and as close as possible to a handbook in terms of applicability. Another feature in common with an extended textbook or a handbook is the rather complete coverage of the topic by the entire series. Certainly, not every volume or chapter will be equally interesting for every reader, but we do hope that several chapters and volumes will be of value for graduate students, for researchers who are young in age or thinking, and for practitioners from industries that are manufacturing or using drying equipment. We also hope that the readers and owners of the entire series will have a comprehensive access not to all, but to many signiﬁcant recent advances in drying science and technology. Such readers will quickly realize that modern drying technology is quite interdisciplinary, proﬁting greatly from other branches of engineering and science. In the opposite direction, not only chemical engineers, but also people from food, mechanical, environmental or medical engineering, material science, applied chemistry or physics, computing and mathematics may ﬁnd one or the other interesting and useful results or ideas in the series. The mentioned interdisciplinary approach implies that drying experts are keen to abandon the traditional chemical engineering concept of unit operations for the sake of a less rigid and more creative canon. However, they have difﬁculties of identiﬁcation with just one of the two new major trends in chemical engineering, namely process-systems engineering or product engineering. Efﬁcient drying can be completely valueless in a process system that is not efﬁciently tuned as a whole, while efﬁcient processing is certainly valueless if it does not fulﬁl the demands of the market (the customer) regarding the properties of the product. There are few topics more appropriate in order to demonstrate the necessity of simultaneous treatment of product and process quality than drying. The series will try to work out chances that emerge from this crossroads position. One further objective is to motivate readers in putting together modules (chapters from different volumes) relevant to their interests, creating in this manner individual, task-oriented threads trough the series. An example of one such thematic thread set by the editors refers to simultaneous particle formation and drying, with a focus on spray ﬂuidized beds. From the point of view of process-systems engineering, this is process integration – several unit operations take place in the same equipment.

Series Preface

On the other hand, it is product engineering, creating structures – in many cases nanostructures – that correlate with the desired application properties. Such properties are distributed over the ensemble (population) of particles, so that it is necessary to discuss mathematical methods (population balances) and numerical tools able to resolve the respective distributions in one chapter of Volume 1. Measuring techniques providing access to properties and states of the particle system will be treated in one chapter of Volume 2. In Volume 3, we will attempt to combine the previously introduced theoretical and experimental tools with the goal of product design. Finally, important issues of energy consumption and process intensiﬁcation will appear in chapters of Volumes 4 and 5. Our hope is that some thematic combinations we have not even thought about in our choice of contents will arise in a similar way. As the present series is a series of edited books, it can not be as uniform in either writing style or notation as good textbooks are. In the case of notation, a list of symbols has been developed and will be printed in the beginning of every volume. This list is not rigid but foresees options, at least partially accounting for the habits in different parts of the world. It has been recently adopted as a recommendation by the Working Party on Drying of the European Federation of Chemical Engineering (EFCE). However, the opportunity of placing short lists of additional or deviant symbols at the end of every chapter has been given to all authors. The symbols used are also explained in the text of every chapter, so that we do not expect any serious difﬁculties in reading and understanding. The above indicates that the clear priority in the edited series was not in uniformity of style, but in the quality of contents that are very close to current international research from academia and, where possible, also from industry. Not every potentially interesting topic is included in the series, and not every excellent researcher working on drying contributes to it. However, we are very conﬁdent about the excellence of all research groups that we were able to gather together, and we are very grateful for the good cooperation with all chapter authors. The quality of the series as a whole is set mainly by them; the success of the series will primarily be theirs. We would also like to express our acknowledgements to the team of Wiley-VCH who have done a great job in supporting the series from the ﬁrst idea to realization. Furthermore, our thanks go to Mrs Nicolle Degen for her additional work, and to our families for their tolerance and continuing support. Last but not least, we are grateful to the members of the Working Party on Drying of the EFCE for various reasons. First, the idea about the series came up during the annual technical and business meeting of the working party 2005 in Paris. Secondly, many chapter authors could be recruited among its members. Finally, the Working Party continues to serve as a panel for discussion, checking and readjustment of our conceptions about the series. The list of the members of the working party with their afﬁliations is included in every volume of the series in the sense of acknowledgement, but also in order to promote networking and to provide access to national working parties, groups and individuals. The present edited books are

XV

XVI

Series Preface

complementary to the regular activities of the EFCE Working Party on Drying, as they are also complementary to various other regular activities of the international drying community, including well-known periodicals, handbooks, and the International Drying Symposia. June 2007

Evangelos Tsotsas Arun S. Mujumdar

XVII

Preface of Volume 2 As indicated in the Preface of this series, Computational tools at different scales were presented in Volume 1 of Modern Drying Technology. However, models need parameters, they must be validated, and they do not always provoke immediate enthusiasm among manufacturing professionals, quality managers and customers. Therefore, even the most sophisticated computational tools are of limited value if not accompanied by equally powerful measurement methods. Volume 2 of the series is, therefore, dedicated to the treatment of the most relevant Experimental techniques discussed in depth in six chapters: Chapter 1: Measurement of average moisture content and drying kinetics for single particles, droplets and dryers Chapter 2: Near infrared spectral imaging for visualization of moisture distribution in foods Chapter 3: Magnetic resonance imaging for determination of moisture proﬁles and drying curves Chapter 4: Use of X-ray tomography for drying related applications Chapter 5: Measuring techniques for particle formulation processes Chapter 6: Determination of physical properties of ﬁne particles, nanoparticles and particle beds Chapter 1 presents experimental techniques such as . . . . . .

By magnetic suspension of the specimen, weight measurements can approach the accuracy theoretically provided by a microbalance. Therefore, the mass of wet single particles, the change in this mass with time in the course of drying and single-particle drying kinetics can be determined accurately, provided that the particle is not too

small. Additionally, dry mass, adsorption isotherms and kinetics of adsorption or desorption can be determined. What the magnetic suspension balance achieves with one particle is achieved by infrared spectroscopy for an entire particle system such as a ﬂuidized bed. By measuring the water concentration in the gas phase at the outlet and the inlet of a dryer, the hold-up of water can be derived precisely. From its change with time the drying kinetics of the particle system are obtained and can be scaled-down to the single particle with some appropriate model. In this way, single-particle drying curves become accessible, even for ﬁne powders. On the other hand, the moisture content of the particle system can be monitored very precisely, which is important for understanding and controlling particle formation in spray ﬂuidized beds. Dew point mirror hygrometry is discussed together with infrared spectroscopy, because the former has been used to calibrate the latter. Coulometry is very accurate in measuring small amounts of water, but takes some time and care, which is a problem if the mass of water has to be determined for every individual particle in a sample consisting of many particles. Such a task corresponds to the measurement of moisture distribution at the outlet of a continuous dryer or in a certain particulate product. It can be solved by using coulometry to calibrate nuclear magnetic resonance, and then performing serial measurements by NMR, which is faster and more comfortable. Finally, if single droplets are to be investigated rather than porous particles, then acoustic levitation – which is capable of suspending a small object in a ﬂuctuating pressure ﬁeld of the gas phase – is the method of choice. Drying kinetics can be derived from the optically recorded decrease in droplet diameter with time, from the slight change in the distance between the center of the droplet and the pressure ﬁeld node with droplet weight, or from measured outlet gas moisture contents in the case of a slight gas sweep. The technique can be validated with drops of pure water and then applied to obtain data on the drying behavior of multicomponent liquid mixtures. Despite their capabilities, the methods from Chapter 1 cannot provide insight into the interior of particles or other porous bodies. Other experimental approaches are necessary for this purpose, and are discussed in the subsequent Chapters 2, 3 and 4. The approach of Chapter 2 makes the sacriﬁce of cutting the sample into very thin slices. This sacriﬁce is rewarded by the fact that such thin slices can be illuminated, and absorbance spectra (the so-called hyperspectrum) can be recorded in the nearinfrared region. Calibration, spectroscopic data processing and image analysis provide images of the distribution of the constituents in space. The target constituent can be water (or rather ice, because the sample is usually frozen before treatment in the micro-slicer) as demonstrated with measured distributions of moisture in soybean seeds. However, the method can also visualize the distribution of other constituents, such as sugar, pigments or foreign substances in food materials. Chapter 3 is dedicated to magnetic resonance imaging – a non-invasive method that does not require destruction of the sample. First, the principles of the method and the way from the simple determination of total water in Chapter 1 to spatial distributions of water content in one, two or three dimensions are explained.

Preface of Volume 2

Then, several applications of MRI to paper, pulp and wood materials are discussed – some of them by reference, some others in considerable detail. The measurement of moisture proﬁles across multilayer cardboard samples during drying is very thoroughly presented. This example shows that all the information attainable by rather conventional methods (especially the drying curve) can also be obtained by means of MRI. However, MRI offers more, namely insight into the mechanisms of mass transfer in the product and to differences between such mechanisms. The latter can arise from differences in structure caused by design (e.g. in lamellar composites), by manufacturing (e.g. by the paper machine) or by nature (e.g. in wood). Apart from moisture distributions, the mobility of water in the drying material can also be obtained by magnetic resonance. The experimental results can unveil the – otherwise invisible – allocation of water within microstructured products. They can also provide diffusion coefﬁcients that can be correlated with moisture content and used in improved models for the process. Finally, applications of MRI to studies of the drying of agricultural and food materials are presented. Structural heterogeneity and anisotropy are rather the rule than the exception for this class of products, they correlate with moisture distribution, especially in the case of efﬁcient drying processes at relatively high temperatures, and can give rise to non-uniform shrinkage, stresses and damage. Poor properties of dried gels or broken paddy rice kernels are possible consequences that must be avoided, wherein MRI can be an important help. Since this requires a careful application of the method, limitations and possible pitfalls are critically addressed throughout Chapter 3. Chapter 4 discusses X-ray tomography, which is an alternative to MRI. Whereas MRI is based on emission by speciﬁc nuclei after appropriate excitation, attenuation by various species is the basis of X-ray tomography. Attenuation is made to tomography by rotation and reconstruction. Rotation provides views from different directions through the object, creating a spatial grid from the intersection points of the respective beams. Reconstruction computes (therefore: computed tomography) from integral attenuation data (from the single views) the attenuation taking place locally, in every volume element of the grid. Since the attenuation depends on the kind and amount of atoms present, spatial distributions of constituents can be obtained in the next step. Such constituents can be the solid and the liquid phase during drying. Observation of the distribution of the liquid phase provides – as previously discussed – insight about drying mechanisms and kinetics. Observation of the solid phase can help to quantify shrinkage, identify cracks, and correlate structural changes with product and process properties. Convective drying of sludge, convective drying of carbon gel monoliths and vacuum contact drying of pharmaceuticals are the examples used in Chapter 4 to explain the application of X-ray CT. Furthermore, methodic aspects such as image ﬁltering and segmentation, and the derivation of morphological characteristics are treated. Equipped with the methods of Chapters 1 to 4, we can (hopefully) understand drying much better, but we still do not have satisfactory access to, for example, how products emerge from processes that combine particle formation with drying, how

XIX

XX

Preface of Volume 2

particles move in dryers, or how powders ﬂow during processing, handling or ﬁnal use. To answer such questions we must widen our horizon from drying as a unit operation to drying as a part of solids processing and particle technology. This includes the use of various additional experimental techniques, as described in Chapters 5 and 6. A large part of Chapter 5 focuses on experimental techniques which originate from the investigation of particle formulation processes coupled with drying (wet granulation, agglomeration or coating) in ﬂuidized, spout-ﬂuid or spouted beds. These are: . . . . . . . .

Modiﬁed spatial ﬁltering is a laser-optical technique to measure in-line particle size and velocity. It is explained with applications to continuous spray ﬂuidized bed granulation of detergents and batch granulation of pharmaceuticals. Dynamic image analysis is an off-line optical method that provides particle size and shape. Particle detection by image analysis is used to see particles and bubbles, to calculate porosities and to map the spatial distribution of the phases in the particle system. However, it works only near some transparent wall, so that it is applicable only to essentially two-dimensional geometries, like spouted beds. Particle image velocimetry is subjected to the same restriction, but provides more information, namely particle velocities. Unlike convectional PIV, it does not require the addition of a tracer, because the product particles themselves fulﬁll this function. Global information about phase distribution, dynamic behavior, stability and bubbling state of the entire particle system (e.g. ﬂuid-spout bed) can be extracted from pressure drop ﬂuctuations by Fourier transform of the frequency spectra. More speciﬁc insight into the particle system is provided by positron emission particle tracking. The particle to be tracked becomes detectable by the emission of g-rays, which results from the decay of a radioactive marker. In this way position trajectories can be obtained, collision events can be identiﬁed and particle velocities can be calculated. Particle velocity ﬁelds are also accessible – after calibration – by means of the ﬁber optical probe. This probe is equipped with both emitting and detecting optical ﬁbers, and can be inserted in the bed like an endoscope. The jet zones created by spray nozzles in ﬂuidized beds can be identiﬁed and investigated in this way. Finally, attrition dust and overspray created in spray ﬂuidized beds can be detected at the gas outlet, either by appropriate selection and conventional analysis (isokinetic sensor) or by aerosol spectroscopy (on-line particle counter). The remaining part of Chapter 5 gives a more general overview of the mechanics of wet or dry granular media (interparticle forces, mechanical interactions, elastoplastic

Preface of Volume 2

behavior, failure properties), including references to a large number of methods for measurement and testing. After the transition provided in the last part of Chapter 5 and with a certain intended overlap, Chapter 6 treats the characterization of ﬁne particles, powders and particle systems from the point of view of general particle technology. Many experimental techniques are discussed, such as . . . . . . . .

Laser scattering and diffraction provide size distributions of dilute particle ensembles, whereas in dense particle systems the same objective can be attained by ultrasonic spectroscopy methods. Solid density, surface area and pore size distribution of either powders or consolidated porous bodies can be obtained by a combination of pycnometry with gas adsorption techniques. Particle interaction devices based on the principle of atomic force microscopy can give direct insight into the forces acting between particles in contact. The same forces are manifested in the results of free fall, impact or compression measurements, which can be translated to restitution coefﬁcients, to probabilities for breakage, abrasion or attrition, and to size distributions (selection functions) for the resulting fragments. Furthermore, the forces between particles in contact deﬁne the ﬂow of powders and granules, which – in turn – become visible by shear testing. Therefore, several shear testing facilities and their use are presented in detail in Chapter 6, along with a thorough treatment of the mechanics of cohesive powders and preconsolidated materials. High-speed cameras are indispensable for free fall or other impact measurements, but they can also be used to track the movement of particles in some types of equipment, such as rotary drums. Chapter 6 ﬁnishes with the presentation of such results, which are of interest for contact dryer operation. Several topics considered from the computational point of view in Volume 1 are further treated in Volume 2 with respect to experimentation. To these belong: .

As pointed out in the general preface, thematic threads, multiscale considerations and interdisciplinary approaches are essential common features of the Modern Drying Technology series. Concerning the scales, Chapter 1 of Vol. 2 concentrates on particles and particle systems. The focus of Chapters 2 to 6 remains on particles and particles systems, however, the resolution of several experimental methods presented in these chapters reaches down to the pore scale. Measuring principles for some methods arise from the atomic or sub-atomic level and the results of some others reﬂect molecular scale phenomena. Links to food engineering, electrical engineering, medical engineering, physics, mechanics, and material science are especially pronounced in Volume 2. A key feature of this volume is that – dealing with experimental techniques – it does not only refer to scientiﬁc principles but, often, also to commercial equipment. This cannot be avoided, because all authors report primarily about their own experiences with measurements, which have been gained with speciﬁc instruments. Therefore, mention of the types and company names are useful pieces of information for documentation. It is neither indication of a preference, nor recommendation, and certainly not advertisement or endorsement of the product. In the same context it should be stressed that discussion of some rather expensive experimental techniques does not imply that good research is a privilege of the well-endowed institutions. On the contrary, it is the ﬁrm opinion of the editors that good science is done by good scientists, who understand the currently available tool-boxes and wisely select those instruments that a certain problem requires and deserves. As to the acknowledgements, they are for Volume 2 identical to those in the series preface. We would like to stress them by reference, but not repeat them here. July 2008

Alternative symbols are given in brackets Vectors are denoted by bold symbols, a single bar, an arrow or an index (e.g., index: i) Tensors are denoted by bold symbols, a double bar or a double index (e.g., index: i, j) Multiple subscripts should be separated by colon (e.g., rp;dry : density of dry particle)

Knowledge of the amount of moisture contained in particles before, during and after drying is an elementary requirement in drying technology. This moisture amount, for example for quality control, can easily be determined on more or less large samples of particles by weighing. However, other tasks, such as the design of industrial convective dryers impose much more serious challenges. To reliably design a convective industrial dryer, kinetic data referring to the speciﬁc product are necessary. Since information on drying kinetics is usually not available, it has to be gained experimentally. In this case, it is not sufﬁcient to measure the mass of moisture contained in the product at a certain point of time, but the change of this mass with time has to be resolved as accurately as possible. Additionally, the change of mass with time must refer to the single particle. The reason for this second requirement is that gas conditions change in particle systems. This results – even if every particle has exactly the same properties and the particles are perfectly mixed – in more or less signiﬁcant differences between the drying kinetics of the entire particle system and the drying kinetics of the single particle. Experimental techniques for the determination of single particle drying kinetics will be discussed in Section 1.2, with emphasis on the magnetic suspension balance. On the other hand, it is evident that measurements on single particles will give only very low signals and, hence, be confronted with severe limitations of resolution and accuracy, even when using very sensitive instruments. This is especially true for small particles (powdery products). Therefore, we may be forced to investigate drying kinetics of an entire particle system such as a packed or ﬂuidized bed. This is typically done by measuring gas humidity at the outlet of the dryer, instead of solids moisture content. It should be borne in mind that the results of such indirect measurements must be scaled down to the single particle by an appropriate model in order to obtain unbiased access to product-speciﬁc drying kinetics. Important instruments for

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

2

measuring gas humidity (infrared spectrometer, dew point mirror) will be presented in Section 1.3 along with some examples of scaling down. Even if we are not interested in drying kinetics, but merely in quality control, measurement of the amount of moisture contained in a sample may not be sufﬁcient. The reason is that the particles have a more or less broad residence time distribution in continuous dryers, which results in a moisture distribution in the outlet solids. This kind of distribution can only be resolved by measuring the moisture content of many individual particles. Methods for accomplishing this non-trivial task, namely coulometry and nuclear magnetic resonance, are the topic of Section 1.4. In the same section, an example of modeling the distribution of moisture in dried solids (in a population of particles) will be given. Until Section 1.4 it is assumed that the product to be dried consists of solid particles containing moisture in their porous interior. While this is true for many drying processes, the feed of some others – namely spray drying – is a liquid. Determination of drying kinetics for the droplets cannot be conducted with the same methods as for solid particles, but requires the application of speciﬁc measuring techniques. This topic will be covered in Section 1.5 by detailed discussion of acoustic levitation. Common to all the experimental techniques of the present chapter is that they do not provide immediate access to the moisture proﬁles developing in the interior of particles, droplets or other bodies during drying. Direct measurement of such proﬁles requires other experimental approaches, which will be presented in Chapters 2–4.

Before presenting the magnetic suspension balance as a modern instrument for measuring single particle drying kinetics a short review of other methods, which can be used for the same purpose, will be given. These involve the use of . . .

a conventional microbalance a balance in combination with a drying tunnel an acoustic levitator.

A straightforward method to measure a drying curve is to put one wet particle on a conventional microbalance and record its change in weight (Hirschmann and Tsotsas, 1998). To avoid heat transfer from the plate of the balance, a miniature wooden stand can be used. The particle is ﬁxed in the crossbeam of this stand between the sharp tips of very thin wood bars. In this way, it is surrounded by air, providing uniform heat and mass transfer from all sides. However, such measurements are limited to ambient conditions and difﬁcult to reproduce exactly.

1.2 Magnetic Suspension Balance

When hanging the specimen in a drying tunnel, connection to the balance must be provided by means of a cord or thin wire. Since forces and force ﬂuctuations are transferred in this way from the specimen to the balance, a certain noise in the data is unavoidable, so that it does not make sense to use the most accurate microbalance. Therefore, a common balance with a sensitivity of merely 0.1 mg was used by Groenewold et al. (2000). The specimen consisted of 50 particles glued at sufﬁcient distance from each other on a net of watertight material, as proposed by Blumberg (1995). Due to the distance between the individual particles, the measurement can be assumed to closely approximate single particle kinetics. Experiences with the mentioned gravimetric methods are summarized in Tab. 1.1. As this table shows, both methods are limited with respect to operating conditions such as gas temperature and gas velocity. Measurement up to the relatively high gas velocity of 2 m s1 indicated in Tab. 1.1 for the drying tunnel is possible only by post treatment of the primary experimental results. This smoothing has been performed by averaging and a cubic spline, as proposed by Kemp et al. (2001). A serious further limitation concerns the minimum size of particles that can be investigated – due to both balance accuracy and difﬁculties in handling and ﬁxing objects smaller than about 1 mm. Co-axial ﬂow with respect to the hanging sample (DaSilva and Rodrigues, 1997; Looi et al., 2002) may have some advantages in comparison to crossﬂow against the specimen in the drying tunnel, but it is not fundamentally different. The difﬁculty common to all gravimetric methods arises from the requirement of suspending the particle in gas while simultaneously measuring its weight by connection to a balance. One solution is to refrain from gravimetric measurement and concentrate all efforts in reasonably suspending the particle in a ﬂow ﬁeld. This leads to acoustic levitation. The principles of acoustic levitation and its application to droplets will be discussed in detail in Section 1.5. Here, it should just be mentioned that the method has also been applied for particles by Groenewold et al. (2002) using a closed 45 kHz instrument. For better stability, a liquid droplet was suspended ﬁrst and the wet particle was then placed in this droplet. To determine the evaporation rate a small air purge was applied, and the change of outlet air humidity was measured by means of a high accuracy dew point mirror. This is very similar to the procedures that will be discussed in Section 1.3. Experiences from these measurements are also summarized in Tab. 1.1. They reﬂect problems of stability of suspension at high

Tab. 1.1 Applicability of different methods for the determination of single particle drying kinetics according to Kwapinski and Tsotsas (2006).

Method

dp, mm

T, C

Flow velocity, m s1

Microbalance Drying tunnel Levitator Magnetic suspension balance

min. 1 min. 1 1–2 min. 1

20–30 30–60 max. 30 max. 350

0 max. 2 0.02–0.065 max. 1

j3

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

4

temperatures and strong purges, which would evidently destroy the oscillating pressure ﬁeld and, thus, also the suspension force acting on the particle. An alternative strategy is to still use a balance, but refrain from any material connection between specimen and weight measuring cell. The realization of this idea in a magnetic suspension balance will be discussed in the following. 1.2.2 Configuration and Periphery of Magnetic Suspension Balance

A schematic representation of the principle of a magnetic suspension balance (MSB) is shown in Fig. 1.1. As already mentioned, the force to be measured is transmitted in a contactless way from the specimen to the microbalance. This is achieved by means of a magnetic force coupling, consisting of an electromagnet and a permanent magnet. The fact that the measuring device is disconnected from the sample chamber enables the microbalance to be kept always under ambient conditions, while high temperatures (up to 350 C) and high pressures (up to 500 kPa) may be realized in the sample chamber. The MSB used by the authors was produced by Rubotherm (Bochum, Germany). It is equipped with a feature called measuring load decoupling, which is conducted by ﬁrst lowering the suspension magnet in a controlled way to a second stationary position a few millimeters below the measuring position. Then, a small carrier to which the sample is connected is set down on a support. Now the sample is decoupled from the balance. The suspension magnet is in a freely suspended state, and only its own weight is transmitted to the balance. This so-called zero point position, which corresponds to an empty balance pan in a normal weighing procedure, allows for taring and calibration of the balance at all times, even when recording measurements

Fig. 1.1 Schematic representation of the MSB.

1.2 Magnetic Suspension Balance

under process conditions in the measuring cell. The resulting correction of zero point and sensitivity drifts increases the measuring accuracy signiﬁcantly, especially in the case of long term measurements (Rubotherm, 2004). Apart from drying kinetics, chemical reactions (polymerization, decomposition, combustion, corrosion), formulation processes (e.g. coating), phase equilibrium (e.g. sorption) and material properties (surface tension, density) can also be investigated in the MSB. The conﬁguration installed in the laboratory of the authors (Fig. 1.2) is used mainly for determination of drying kinetics or sorption equilibrium. Therefore, it includes a periphery capable of establishing different atmospheres of conditioned air. The design of this humidiﬁer is identical to the set-up for calibration of IR spectrometers that will be described in Section 1.3.4. Additionally to the measurement of weight, gas humidity can be measured at the inlet of the MSB (after the air conditioner) and at the outlet of the MSB by means of a dew point hygrometer and an IR spectrometer, respectively. The gas feed can be pressurized air with a moisture content of 0.5 g kg1 or completely dry ﬂask gas. Mass ﬂow rates are adjusted by a mass ﬂow controller, calibrated by means of a ﬁlm ﬂow meter. A correction for buoyancy should be applied to MSB data according to the relationship (Rubotherm, 2004): ML ¼ MBL þ V L rg

ð1:1Þ

Here, ML and VL are the mass and volume of the load (including load cage and basket), respectively; MBL is the value of the balance display and rg is the gas density.

Fig. 1.2 Experimental set-up of magnetic suspension balance (MSB).

j5

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

6

Furthermore, for drying samples in the range of milligrams the buoyancy of the sample should be taken into account. Thus, the expression MS ¼ M BLS ðP; T; wÞM BL ðP; T; wÞ þ V S rg ðP; T; wÞ

ð1:2Þ

can be used to calculate the mass of the sample, MS. Here, MBLS is the value that the balance displays with sample, MBL is the value that the balance displays without sample and VS is the volume of the dry sample. The inﬂuence of changing state variables in the sample chamber (pressure P, temperature T, relative humidity w) is considered in Eq. 1.2. However, the buoyancy effect contributed by water (moisture), which is usually less than 1 mg, is neglected. 1.2.3 Discussion of Selected Experimental Results

In the following, applications of the magnetic suspension balance are illustrated on the basis of results by Kwapinski (Kwapinski and Tsotsas, 2004a, b, 2006). The materials used in these experiments (molecular sieve 4A, g-Al2O3 and SiC) have very different pore diameters, see Tab. 1.2. Zeolite and alumina oxide are highly hygroscopic, while silicium carbide has very low hygroscopicity. Figure 1.3, as an example, shows results on the kinetics of desorption of water from one single particle of zeolite 4A. This particle with a diameter of 2 mm was ﬁxed with glue onto the tip of a thin needle suspended in the sample chamber of the MSB. First, water was adsorbed on the particle by exposing it to air with a relative humidity of w0 ¼ 0.60. Then, the experiment was started by suddenly reducing the relative humidity of the air from this initial value to a value of win ¼ 0.05 at the inlet of the sample chamber. The progress of particle moisture content until reaching the new, lower equilibrium value is plotted in Fig. 1.3 for different gas velocities. To obtain results representing the kinetics of mass transfer in the interior of the particle, it is desirable to reduce the relatively small inﬂuence of gas-side mass transfer as far as possible by measuring at high gas velocities. This, however, has an adverse effect on the accuracy of weighing, so that a compromise must be found. In this context, it should be mentioned that the ﬂow of conditioned air during the presented experiments was from the bottom to the top of the sample chamber. This creates a ﬂow force on the particle – similar to the buoyancy force. Consequently, smaller indications of mass are obtained by the balance with increasing ﬂow velocity. The resulting minor error can be corrected by calibration, so that weighing results independent of ﬂow Tab. 1.2 Selected properties of experimental materials.

dp, mm dpore, mm rp, kg m3 ep, %

zeolite 4A

c-Al2O3

SiC

2.0 and 5.0 0.0004 720 33.5

1.4 0.01 1040 70–75

1.0–1.8 0.12–5.1 1610–2330 25–49

1.2 Magnetic Suspension Balance

Fig. 1.3 Experimental desorption curves of water from 4 A zeolite at 25 C; Comparison of process kinetics for different velocities of the air.

velocity are obtained. Even without correction, the results are sufﬁcient for many practical applications. The results of similar experiments with a single particle of g-Al2O3 are depicted in Figs. 1.4 and 1.5. Here, the ordinate shows directly the mass, which decreases during desorption of water. The relative random error of measurement by the MSB is indicated. This error increases with increasing gas ﬂow velocity, but is still reasonably small at u ¼ 0.2 m s1. On the other hand, such a velocity is sufﬁcient for the process to take place in the particle-side controlled regime. Experiments with bigger particles

revealed that the relative error increases with particle size for the same gas velocity. The reason is the larger vibrations of large particles. Though still occurring, such vibrations are better damped in the MSB than in other gravimetric devices, due to the indirect contact by the suspension magnet. The mentioned relative error also depends on the moisture load, which is changing during the desorption process, and differs for different particle sizes and materials. Figure 1.6 presents results for the materials of Tab. 1.2 under otherwise the same conditions. All materials were conditioned at T ¼ 25 C and w0 ¼ 0.30. At t ¼ 0 there was a sudden change of relative humidity of the ﬂowing air to win ¼ 0.05. The amount of water that can evaporate from zeolite is deﬁned as unity in Fig. 1.6 and is larger than for the two other materials. The relative error for SiC, with a total water loss of

Fig. 1.6 Desorption data for zeolite 4A, g-Al2O3 and SiC.

1.2 Magnetic Suspension Balance

about 10 times less than zeolite, will be proportionally larger. This ratio is not constant, but depends on the operating conditions. It should, however, be pointed out that SiC is usually considered to be completely non-hygroscopic. In fact, the weak hygroscopicity indicated by Fig. 1.6 could not be detected by conventional gravimetric methods, but can be detected in the MSB. Using the MSB it is also possible to gain equilibrium data. Examples of isotherms for the adsorption of water on molecular sieves are shown in Fig. 1.7. In such experiments, more than one particle may be placed into a basket, suspended from the balance. Even with many particles in the basket, the time to reach a constant mass is much shorter than required by conventional methods, due to the favorable ﬂow of conditioned air. The temperature range of Fig. 1.7 can be widened to 350 C. Such high temperatures and vacuum may be necessary to determine the mass of dry particles, that is, the reference in the deﬁnition of solids moisture content. To ﬁnd this mass, experiments as depicted in Fig. 1.8 were made. Initially, the temperature should be raised slowly to 100 C in an environment of N2. After 100 C the temperature can be increased more quickly. In the presented experiment this was done stepwise. The temperature trajectory should, ideally, be piecewise linear, but, in reality, some inertial effects and overshooting are present. The ﬁnal measurement was taken at 350 C and in vacuum, after the mass had reached a constant value. The change of condition at the end of the experiment from dry gas at ambient pressure and small ﬂow to vacuum is the reason for the small jump in the mass indication. This is due to the removal of the ﬂow and represents the small inaccuracy that has been previously discussed and can be corrected by calibration. Recent work (Suherman, 2007; Suherman et al., 2008) shows that the drying kinetics of single polymer granules with diameters from 2.5 to 2.9 mm can be measured with good reproducibility by using the MSB. The accuracy of the instrument under speciﬁc operating conditions can be evaluated by time series analysis and other statistical methods. Furthermore, it is shown in this work how the time series analysis can contribute to a reliable identiﬁcation of the end of the drying process.

Fig. 1.7 Isotherms for adsorption of water on zeolite 4 A.

j9

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

10

Fig. 1.8 Measurement for the determination of the mass of dry zeolite by use of the MSB.

This helps to accurately determine dry mass. Statistical methods can also support data smoothing. Instead of the previously mentioned cubic splines, Suherman (2007) used the moving average technique to this purpose. By smoothing the primary data the signiﬁcance of measurements can be extended towards smaller moisture contents at the end of the drying process. A coarse estimation of the applicability range of the MSB is given in Tab. 1.1. Concerning this table, it should be noticed that the maximum operating velocity of u ¼ 2 m s1 assigned to the drying tunnel could be attained only in combination with numerical smoothing of the primary data. In contrast, gas velocities of up to u ¼ 1 m s1 can be realized in the MSB without smoothing. Without smoothing, the MSB has an advantage with regard to the maximum possible gas velocity. Nevertheless, such information is only indicative, because the applicability range shrinks unavoidably with decreasing particle diameter, due to the decrease in weight. Additionally, it becomes more and more difﬁcult to ﬁx one particle without signiﬁcant contact with some solid support. Consequently, the applicability of all gravimetric methods – including the MSB – ends at a particle diameter of about 1 mm. For powdery materials with much smaller particle size alternative methods are needed. Such alternatives will be discussed in the following section.

As discussed in the previous section, the determination of the drying kinetics of materials with a particle size below 1 mm can hardly be conducted by single particle experiments; the accuracy and resolution of the methods available for this purpose

1.3 Infrared Spectroscopy and Dew Point Measurement

are not high enough. Consequently, it is necessary to measure the temporal change in moisture content of an entire particle system and then extract from this information single particle drying kinetics. The particle systems considered are packed beds and ﬂuidized beds. The use of a packed bed corresponds to the well known thin layer method (TLM, see, e.g. Hirschmann et al., 1998). In TLM a shallow packed bed is placed on a sieve with air ﬂow in the direction of gravity. The moisture content of the packed bed is measured by interrupting the experiment and weighing. Alternatively, outlet gas humidity can be measured and used to calculate the corresponding change in the moisture content of the solids. Even for very thin layers the results of this method cannot be set equal to single particle drying kinetics, but have to be scaled-down to the single particle by an appropriate model. Such modeling is not trivial, due to axial dispersion in the gas ﬂowing through the packed bed. Additionally, it is difﬁcult to prepare a particle layer of small but uniform thickness. Differences in thickness lead, however, to ﬂow maldistribution, because the gas prefers pathways of minimal bed thickness and, thus, minimal ﬂow resistance. Such ﬂow bypasses can hardly be modeled. Moreover, they depend on the skills of the person who has prepared and conducted the experiment. Gas bypass is also present in a ﬂuidized bed, due to bubbling. However, this bypass is a property of the particle system – rather independent from the operator. Furthermore, reliable models are available for scaling ﬂuidized bed drying results to the single particle. Because of these advantages, the route from ﬂuidized bed measurements to single particle drying kinetics will be discussed in detail in this section. The ﬁrst step is the determination of the change in solids moisture content in the ﬂuidized bed with time. Conventionally, one takes samples out of the bed during the drying process and measures the moisture content by weighing. This is intermittent, changes the hold-up and provides just a few points along the drying curve of the ﬂuidized bed. Therefore, it is better to determine the decrease in solids moisture content in the ﬂuidized bed dryer indirectly, by measuring the gas moisture content at the outlet. For the simple case of a batch dryer one needs to quantify the moisture content of the gas at the inlet and at the outlet of the dryer and the mass ﬂow rate of the dry ﬂuidization gas. The evaporation ﬂow rate is then given by _ g ðY out Y in Þ _v¼M M

ð1:3Þ

Taking into account the initial moisture content of the solids X0, the temporal change of moisture can be determined from ð 1 _ g ðY out Y in Þdt X ðtÞ ¼ X 0 ð1:4Þ M M dry Obviously, the measurement of the gas moisture contents Yout and Yin determines the quality of the method. Before discussing this measurement, by infrared spectroscopy and dew point determination, a short outline of the experimental set-up will be given.

j11

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

12

1.3.2 Experimental Set-Up

A schematic diagram of the laboratory scale ﬂuidized bed dryer used in our work is presented in Fig. 1.9. The cylindrical ﬂuidization chamber has an inner diameter of 152 mm. A sintered metal plate with a pore size of 100 mm serves as the air distributor in order to ensure a uniform ﬂow of ﬂuidization gas. To control the gas inlet temperature the apparatus is equipped with an electrical heater. For granulation or agglomeration processes a two-component nozzle with an adjustable gas ﬂap (Type 970/0 S4, Schlick Co.) is installed. The liquid is delivered to the nozzle by a piston pump (Sewald Co.). Pressurized air is used as the ﬂuidization gas in order to attain as constant as possible ﬂow rates. In this way, the variation of mass ﬂow rate could be kept below 0.1 kg h1. Using a blower would lead to signiﬁcantly higher ﬂuctuations. The gas ﬂow rate is measured by means of a mass ﬂow meter (ELFLOW, Bronkhorst M€attig Co.). Additionally, several probes are installed to record temperatures at the gas inlet and outlet, and pressure drops of the distributor plate and the hold-up. As mentioned above, the accuracy of the described approach depends directly on the precision of the measurement of gas moisture content. This requires . .

high accuracy short measurement period.

Both requirements can be fulﬁlled by employing infrared (IR) spectroscopy. In our case, two IR spectrometers of type NGA 2000 MLT (EMERSON Process Management Co.) were installed at the inlet and at the outlet of the ﬂuidization chamber.

Fig. 1.9 Scheme of fluidized bed dryer.

1.3 Infrared Spectroscopy and Dew Point Measurement

1.3.3 Principle of Measurement with the Infrared Spectrometer

The basis of IR spectroscopy is absorption of infrared radiation caused by the gas being measured. While the wavelengths of the absorption bands are speciﬁc to the type of gas, the strength of absorption is a measure of concentration. By means of a rotating chopper wheel, the radiation intensities coming from the measuring and the reference sides of the cell of the instrument produce periodically changing signals within a detector. The detector signal amplitude thus alternates between concentration dependent and concentration independent values. The difference between the two is a reliable measure of the concentration of the absorbing gas component. Figure 1.10 depicts a scheme of the IR spectrometer. A heating coil in the light source (1) generates the necessary infrared radiation. This radiation passes through the light chopper wheel (2) and a ﬁlter cell (4) that screens interfering wavelengths out of the radiation spectrum. Due to the shape of the chopper wheel, irradiation of equal intensity alternates between the measuring side (6) and the reference side (7) of the analysis cell (5). Only the measuring side is swept by the gas to be analyzed. Subsequently, the radiation passes individual optical ﬁlters around a second ﬁlter cell (8) and reaches the pyro-electrical detector (10). This detector compares the measuring side radiation, which is reduced because of absorption by the gas, and the

Fig. 1.10 Scheme of IR spectrometer.

j13

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

14

reference side radiation. Cooling and heating of the pyro-electrical material of the sensor lead to an alternating voltage signal. The ﬁnal measuring signal of the IR spectrometer is equivalent to the volume concentration of the absorbing gas component. In our case, this component is water vapor. Volume concentration is equal to molar fraction ~y, which can be converted into the mass moisture content by the relationship Y¼

~ w ~y M ~ g 1~y M

ð1:5Þ

1.3.4 Dew Point Mirror for Calibration of IR Spectrometer

To achieve the highest precision for the determination of the moisture content in the gas phase the IR spectrometers need to be calibrated frequently since the pressure in the measuring chamber and, therefore, also the measured volume concentration of water, depend on the ambient pressure. For the calibration, a gas ﬂow with deﬁned moisture content must be supplied to the IR spectrometers. The accuracy of calibration of the spectrometers will depend directly on the accuracy of the measurement of moisture of the provided calibration gas. Dew point mirrors are amongst the most established and recognized devices for the precise determination of moisture content in gases, because of their simplicity and the fundamental principle employed. From the measured dew point temperature Tdp, the saturation pressure p of the water and hence the moisture content can be acquired: Y¼

~ w p ðT dp Þ M ~ g Pp ðT dp Þ M

ð1:6Þ

In a dew point instrument a gas sample is conducted into the sensor cell that contains a miniature temperature-controlled polished metal mirror (Fig. 1.11). This

Fig. 1.11 Operating principle of a dew point mirror.

1.3 Infrared Spectroscopy and Dew Point Measurement

mirror is made of a highly conductive material, typically copper, and plated with an inert material such as gold. It sits on a solid-state thermoelectric heat pump cooling by means of the Peltier effect. As the temperature of the mirror drops and reaches the dew (or frost) point temperature, water is pulled out of the vapor phase of the sample gas and water droplets (or ice crystals) nucleate on the mirrors surface to form eventually a uniform condensation layer. The exact temperature, measured by a platinum resistance thermometer (PRT) directly embedded underneath the mirrors surface, depends only upon the moisture content of the gas and the operating pressure. An optical system, consisting of a visible light emitting diode (LED) and photodetectors, is used to detect the point at which this occurs. The LED provides a light beam of a constant intensity, which is focused by a collimated lens to become the incident beam on the mirror surface, ﬂooding it with a pool of light. Some instruments only detect the reﬂected light using a single photodiode; more sophisticated instrumentation uses a second detector to monitor the scattered light. As dew droplets form on the mirror, the reﬂected light decreases whilst the amount of scattered light increases. The output from each photodiode is digitized with an analog to digital converter to derive numerical representations of the photodetectors. The resulting signals are, in turn, tied into an electronic loop that controls the current applied to the heat pump device. This, in essence, modulates the cooling power to maintain the mirror temperature at the dew (or frost) point of the gas sample. At an equilibrium point, where evaporation rate and condensation rate at the surface of the mirror are equal, the mirror temperature, read by the PRTembedded in the mirror, represents the saturation point for the water vapor in the sample gas, in other words the dew (or frost) point. Whilst the combined condensation of water-soluble gas constituents may be acceptable in small amounts, accumulation of such contaminants over an extended period of time can affect the accuracy of the measurement. Cooled mirror hygrometers usually have the facility to execute a contamination compensation routine to prevent this effect. When the system initiates the dynamic contamination control (DCC) routine, the heat command signal drives the thermoelectric heat pump in reverse, which in turn heats the mirror to a temperature above the dew point to drive off the excess condensate. When the mirror is free from condensation, the optical control loop is typically zeroed to eliminate the effect of contaminants, which may have built up on the mirror surface. Following this re-zeroing of the optical control loop, normal operation of the device is resumed. For mirror temperatures above 0 C, water vapor condenses on the mirror as liquid water (dew point). When measuring temperatures are below the freezing point of water, the condensate can either exist as ice (frost point) or as super-cooled liquid (dew). Whether the condensate is ice or water depends on several factors, such as the purity of the water, the surface morphology of the mirror and the period of time over which the measurement has been made. Alternatively, because of delayed nucleation the condensate may initially appear as a liquid (water) but change into a solid (ice) after a certain period of time.

j15

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

16

For water to freeze, the molecules must become properly aligned to each other, so that it is more difﬁcult to liberate a molecule from ice than from super-cooled liquid water. Therefore, different saturation temperatures are measured for super-cooled water and ice, the former being lower than the latter. This phenomenon affects all cooled mirror instruments and may result in inaccurate interpretation. If the condensate present over a mirror is ice, the mirror temperature at equilibrium will be higher than if the condensate were super-cooled liquid. The errors involved are typically about 10% of water vapor pressure. In order to distinguish between water and ice, some hygrometers are equipped with a microscope which allows the user to visually inspect the surface of the mirror during measurement and look for frost or dew formation. However, the addition of a microscope is usually an expensive option, and it can be difﬁcult to discern water from ice formation, particularly at low dew point temperatures. In the present work an Optidew Vision (Michell Instruments Co.) dew point mirror was used. The measuring range of this dew point hygrometer is from 30 to 50 C with an accuracy of 0.2 K. It is integrated in a device for calibration of IR spectrometers, as depicted in Fig. 1.12. The NGA 2000 IR spectrometer can be calibrated with a simple two-point calibration, since the signal from the pyro-electric sensor is assumed to be linear within the measuring range. Synthetic air from the ﬂask with a dew point of 30 C was used as the so-called zero-gas. The second calibration point was obtained by moistening the synthetic air in a fritted wash bottle to adjust to a dew point of approximately 21 C. The measuring conditions in the analysis cell of the IR spectrometer were controlled in such a way that a gauge pressure of 5 mbar and a ﬂow rate of the sample gas of 400 ml min1 were attained. The ﬂow rate was determined by means of a ﬁlm ﬂow meter (Type SF-2CE, Horiba Stec Co.). The actual values of gas moisture were quantiﬁed by means of the dew point mirror for both calibration points. According to the manufacturer, the accuracy of the IR spectrometer is 1% of the ﬁnal value of the upper limit of the measuring range. By default, the measuring range is set from 0 to 10% volume concentration of water vapor. To increase the accuracy, the upper limit of the measuring range was reduced to 2.8%, which corresponds to a moisture content of 17.92 g kg1. Consequently, the accuracy of measurement of volume concentration is increased to 0.028% so that the moisture content can be

determined with an accuracy of approximately 0.18 g kg1. To prove the linearization of the IR spectrometer three additional dew points were adjusted directly after the calibration. The results, summarized in Tab. 1.3 and depicted in Fig. 1.13, demonstrate that the linear calibration is very satisfactory for the measurement of moisture content. The deviation of the values obtained from the IR spectrometer and the dew point mirror is less than the accuracy of 0.18 g kg1. 1.3.5 Testing the Calibration

As mentioned above, the closure of water balance is essential for the determination of solids moisture content. The closure does not only depend on the measurement of gas humidity but also on the precise determination of gas ﬂow rate and liquid ﬂow rate, whereby the latter is important only in the case of agglomeration and granulation processes. In principle, there are two simple methods to assess the overall accuracy of the instrumentation. The ﬁrst method is a differential approach, where a certain liquid ﬂow rate is injected onto the particles and the instantaneous evaporation rate is quantiﬁed. Under steady state conditions the evaporation rate must be equal to the spraying rate _v¼M _ g ðY out Y in Þ _l¼M M

ð1:7Þ

For the tests the mass ﬂow rate of the ﬂuidization gas and atomizing air of the nozzle was adjusted to 50.61 and 0.89 kg h1, respectively. To minimize the transition time to steady state, non-hygroscopic a-Al2O3 with a Sauter mean diameter d32 ¼ 0.31 mm was used as the bed material. Fig. 1.14a shows the temporal change of gas moisture

Fig. 1.13 Results for testing the linearization of the IR spectrometer.

j17

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

obtained for the three different spraying rates which are summarized in Tab. 1.4. The occasional sharp decrease in outlet moisture content is caused by the switching of the pistons of the pump that feeds water to the nozzle. When this happens, the liquid ﬂow is interrupted for 1 to 2 s, which is readily detected by the spectrometer. Figure 1.14b presents the comparison of the actual spraying rate with the evaporation rate determined by applying Eq. 1.7. As one can see, the deviation is very low. Only for the highest spraying rate was a slight systematic difference observed. To quantify the error of the differential balance, the deviation of spraying rate from evaporation rate _ l M _ g ðY out Y in Þ _v¼M DM

ð1:8Þ

is presented in Fig. 1.15 for undisturbed steady state conditions. As one can see, the error of the differential balance is approximately 2 mg s1 for the ﬁrst two spraying rates, but increases slightly and becomes systematic for the highest spraying rate. The resulting deviations are summarized in Tab. 1.4. In total, it can be concluded that the differential balance is successfully closed, so that the instantaneous evaporation rate can be determined with an accuracy of approximately 3%. The second approach for proving the quality of closure of the moisture balance is an integral method. Here, a certain amount of liquid is sprayed onto pre-dried particles so that the particle moisture content increases. After a certain time the Tab. 1.4 Maximal deviation of differential balance.

_ l [mg s1] M

_ v [mg s1] DM

Error [%]

82.08 110.64 134.23

2 2 þ4

2.43 1.80 þ2.97

1.3 Infrared Spectroscopy and Dew Point Measurement

Fig. 1.15 Calculated deviation of differential moisture balance.

spraying is shut down and the moisture is removed again from the particles. Gas outlet humidity is detected during the entire process. By integral evaluation of these signals the total amount of evaporated water can easily be quantiﬁed: ð _ g ðY out Y in Þdt ð1:9Þ Mv ðtÞ ¼ M For these trials the same test material was utilized as in the previous experiments. The spraying rate was adjusted to 0.13 g s1. Results for two gas ﬂow rates of 50.66 and 30.15 kg h1 are presented in Fig. 1.16 and Fig. 1.17, respectively. Diagram (a) depicts in each case the temporal change of gas moisture content while diagram (b) illustrates the deviation of integral moisture balance obtained from DMv ¼ M l ðtÞMv ðtÞ

ð1:10Þ

The evolution of gas moisture content reﬂects clearly the pre-drying, the spraying and the drying periods. Since the gas mass ﬂow rate was reduced for the second trial,

the gas outlet humidity reaches signiﬁcantly higher values of about 16 g kg1. The initial increase in the deviation of moisture balances indicates the accumulation of water in the bed material. Actually, this value can be directly converted into a moisture content of particles if the dry solids mass is known. The second experiment shows a similar behavior of gas humidity, but a different evolution of DMv. The temporal change in this value indicates that the accumulation of water in the particles increases continuously, even at constant gas outlet moisture. At the end of the experiments – after the drying period – the value of DMv should return to zero. This would mean that we have found in the gas outlet all the water that we have sprayed into the bed and would, thus, correspond to perfect closure of the integral moisture balance. The measured ﬁnal values of DMv are summarized in Tab. 1.5. They show that the error of the integral moisture balance is less than 1% for both cases, which is a very nice validation for the accuracy of the experimental set-up and the instrumentation. 1.3.6 A Case Study: Determination of Single Particle Drying Kinetics of Powdery Material

After successful validation of the instrumentation and the experimental set-up, derivation of ﬂuidized bed drying curves from outlet gas humidity measured by IR spectroscopy will be illustrated. As already discussed, such ﬂuidized bed drying curves can be used – in a second step – to derive single particle drying kinetics of

powdery materials, which is not accessible directly because of their too small particle diameter. To this purpose, drying experiments were conducted with powdery polymer (particle diameter: d ¼ 168 mm, dry particle density: rp ¼ 1123 kg m3). All experiments were carried out under approximately the same process conditions with respect to the mass ﬂow rate of ﬂuidization gas, initial bed mass and gas inlet moisture content. Operating parameters are summarized in Tab. 1.6. Figure 1.18 shows a typical result for the temporal change of moisture content during the drying process. After feeding the wet batch into the apparatus the gas outlet moisture changes rapidly while the inlet moisture (both measured by IR spectroscopy) remains constant throughout the entire experiment. Initially, the outlet moisture exceeds somewhat the theoretical maximum of adiabatic saturation moisture. This phenomenon is caused by the thermal capacity of the apparatus, mainly the air distributor, and the bed material. After a relatively short period the outlet moisture starts to decrease towards the value of the inlet. From this data the temporal change of particle moisture content can directly be withdrawn, taking into account the initial moisture of particles X0. The value of X0 was determined by drying a sample of approximately 40 g in a vacuum oven at 80 C for 24 h. Additional measurement of the ﬁnal moisture content of the solids enables one to check the closure of water mass balance.

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

22

A better way of presenting the results is to use, instead of the plot of Fig. 1.18b, the drying curve, where the drying rate _v¼ m

_ g ðY out Y in Þ M Abed

ð1:11Þ

that refers to the total surface area of the particles is plotted vs. the particle moisture content. Such a diagram is shown in Fig. 1.19a. Direct comparison between drying processes conducted under different process conditions is easier in terms of drying curves because time has been eliminated. To check the reproducibility of results, drying at 50 C was repeated twice. Direct comparison of the data in Fig. 1.19a shows a very good agreement between the two trials throughout the entire experiment. This is additional proof of the reliability of the method. As mentioned above, measurements in a ﬂuid bed dryer do not represent single particle behavior but can be used to scale down to the single particle level by applying an adequate model. In this study, the ﬂuidized bed drying model introduced by Groenewold and Tsotsas (1997) – see also Burgschweiger and Tsotsas (2002), Groenewold and Tsotsas (2007) – has been employed. The model distinguishes between bubble phase and suspension phase. All parameters such as bypass ratio, Sherwood number from particle to suspension phase, and number of transfer units from suspension to bubble phase are set. The only degree of freedom concerns single-particle drying kinetics in the form of a normalized drying curve. This curve is ﬁtted to ﬂuidized bed drying data in the course of scale down. In calculations of ﬂuidized bed drying at conditions other than those used for ﬁtting, single particle drying behavior is an input, so the model works in a fully predictive mode. The inhibition of the drying rate of particles at low moisture contents in terms of single particle drying kinetics can be considered in different ways. One possible approach is normalization in order to describe measured drying curves by reduction to just one normalized (or characteristic) drying curve for the considered product.

This method was introduced for normalization of drying curves measured in batch drying by van Meel (1958), and since then it has been applied in the original or in modiﬁed forms by many authors (van Brakel, 1980; Shibata, 2005; Groenewold, 2004). _ v, The normalized drying rate f is deﬁned as the quotient of the actual drying rate m _ v;I and the drying rate of the ﬁrst drying period m f ¼

_v m _ v;I m

ð1:12Þ

and the normalized solids moisture content, F, is represented by F¼

XX eq X cr X eq

ð1:13Þ

where Xeq is the equilibrium moisture content. Both f and F take values between 0 and 1. Remember that drying is assumed to be gas-side controlled in the ﬁrst and particleside controlled in the second drying period (at X < Xcr). By normalization the two _ v;I ) periods are separated from each other. Gas-side phenomena (i.e. the drying rate m are supposed to be predictable from ﬁrst principles. Particle-side phenomena are described empirically by the function f(F). Successful normalization leads to a function f(F) which is invariant with drying conditions (Tsotsas, 1994; Suherman et al., 2008). Applying this concept, the normalized drying curve of a single particle as well as the critical moisture content are derived by scaling down from measurement results by iterative adjustment in a computer program that implements the ﬂuidized bed drying model. For this derivation the data from experiment 1 (Tab. 1.6) has been used. The normalized drying curve is presented graphically in Fig. 1.19b, with a critical moisture content of Xcr ¼ 0.07 for this product. Figure 1.20 illustrates the opposite exercise, by comparing calculations conducted with the normalized drying curve that has been derived from one experiment with the

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

24

results of three ﬂuidized bed experiments carried out at different gas inlet temperatures. The results show that at high moisture content the measured drying rate is higher than the calculated one. As mentioned above, this is a thermal effect mainly caused by the supply of heat to the ﬂuidized bed from the equipment, in particular from the distributor plate. Before every drying experiment, the entire apparatus is warmed to the inlet gas temperature. After the start of the experiment, heat transfer takes place between the equipment and the drying gas and/or the equipment and the particles, since both the average gas temperature and the particle temperature are clearly lower than the gas inlet temperature in the ﬁrst drying period. As a result of this additional energy, drying rates increase. Towards the end of the drying process, the drying rate reaches very small values, which are still determined from the difference between the outlet and inlet gas humidities. Since the respective measured quantities become almost identical and exhibit a certain noise, scatter of the drying rates is unavoidable at low moisture contents. Nevertheless, the derivation of drying rates appears to be accurate enough till solids moisture contents of about 0.002 in the present experiments. In spite of such restrictions, Fig. 1.20 shows quite good agreement between measurement and simulation in the signiﬁcant range of moisture content. This is true, in particular, for the inﬂuence of temperature. Consequently, the concept of normalization works well for the present example. This is not always the case (Suherman et al., 2008), so that it may be better to use, for example, some diffusion model instead of the normalization method for other products. Then, diffusion coefﬁcients will be the quantities to determine by ﬁtting of the ﬂuidized bed drying model to the experimental results. Apart from this, the described procedure remains essentially the same.

In this section, we address the problem of measuring the relatively low moisture content of a large number of particles on an individual basis with the necessary precision. This problem arises when particulate material is dried and particle moisture at the outlet of the dryer is not uniform. In such a case, the characteristics of the distribution of particle moisture decide the quality of the drying process. In general, the outlet moisture content of any product must be below some speciﬁed value for quality reasons, but over-drying is undesirable because of energy costs, capacity restrictions or product damage. In the following, we choose the example of a continuous ﬂuidized bed dryer (as sketched in Fig. 1.21) to illustrate, ﬁrst, how the moisture content distribution may be approximated by a simpliﬁed population balance model and, then, how it can be measured. Subsequently, measured moisture distributions will be compared with the model.

1.4 Coulometry and Nuclear Magnetic Resonance

Fig. 1.21 Scheme of continuous fluidized bed dryer.

1.4.2 Modeling the Distribution of Solids Moisture at the Outlet of a Continuous Fluidized Bed Dryer

The objective of the present approach is to provide an analytical solution for distributed moisture content of particles at the dryer outlet. To this purpose, we take a certain functional form of the normalized drying curve, Eq. 1.14, and, in contrast to previous studies (Burgschweiger and Tsotsas, 2002; Kettner et al., 2006), do not include energy balances for the solid phase or any balances for the gas phase. Particles (of uniform diameter dp and density rp) are conveyed into the dryer at a constant particle ﬂow rate N_ 0 , all having the same initial moisture content X0. Discharge of particles is by an internal weir pipe, the height of which controls the total hold up of solids (Nbed particles). Furthermore, the dryer is assumed to be sufﬁciently small so that the spatial distribution of solids has no inﬂuence. In this case, particles with the same residence time t also have the same moisture content X(t) and the residence time distribution of the particles in the dryer (corresponding to that of a continuous stirred tank reactor) is the only reason for a distribution of moisture content. For the drying kinetics of a single particle, we assume the functional form of the normalized drying rate 8 > for F 1 < 1 _v m ð1:14Þ ¼ f ¼ pF _ v;I > m for F < 1 : 1 þ Fðp1Þ _ v is the particle drying rate and where p is an adjustable parameter, m _ v;I ¼ rg bðY as YÞ m

ð1:15Þ

is the rate of the ﬁrst drying period (rg: dry gas density, b: gas-side mass transfer coefﬁcient, Yas: adiabatic saturation moisture, Y: moisture content in the bulk of the

j25

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

26

Fig. 1.22 Influence of parameter p on normalized drying curve of single particle.

Typical results are plotted as normalized distributions Q0 ¼ N/Nbed in Fig. 1.23 for the operating parameters given in Tab. 1.7 and different single particle drying curves (by variation of p). For particle moistures X > Xcr, the curves are identical, since the drying rate of the ﬁrst drying period is independent of p. In the second drying period, however, the distributions differ signiﬁcantly. A decrease in the value of p, which corresponds to a decrease in drying rate, shifts the distribution to

1.4 Coulometry and Nuclear Magnetic Resonance

Fig. 1.23 Normalized cumulative number distributions of particle moisture for different values of parameter p (remaining parameters according to Tab. 1.7).

higher moisture contents. Moreover, the width and shape of the distribution are also strongly affected. 1.4.3 Challenges in Validating the Model

In the experiments for testing the above model, g-Al2O3 beads with Sauter diameter dp ¼ 1.8 mm and particle density rp ¼ 1040 kg m3 are used. Since the initial moisture content of these particles is around 0.65, the water contained in a single particle is at most around 2 mg. After drying, most of this moisture will have been removed so that we need a method to detect amounts of water in the range of a few hundred mg with good precision. Gravimetric methods have here reached their limit: the relatively high dry particle mass of 3.2 mg and strong hygroscopic behavior of the Tab. 1.7 Parameter settings for the curves of Fig. 1.23.

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

28

Fig. 1.24 Measurement principle of coulometer for detecting water in solid samples.

material (leading to signiﬁcant moisture uptake during weighing) prevent an accurate measurement of moisture content. When searching for an appropriate measurement method, we also have to bear in mind that a sufﬁcient number of particles (at least 100) have to be characterized for a reliable comparison of experimental and theoretical distribution functions. In the following, we present the methods of coulometry and nuclear magnetic resonance; we will see, by analysis of their advantages and disadvantages, that a combination of both techniques is suitable for fast and accurate moisture measurements. 1.4.4 Coulometry

The principle of coulometry is to determine the quantity of a species by measuring the electric charge Q (in Coulomb) required to completely decompose this species by a well-known electrolytic reaction. Since small electric currents can easily be controlled, measured and integrated over time, the method is suitable for detecting very small species quantities. For example, an electrolysis current of 1 mA reduces water into hydrogen and oxygen at a rate of merely 0.0933 mg s1. The ﬁrst electrolytic cell to continuously measure small amounts of water in gas ﬂows was proposed by Keidel (1959) who already anticipated a wide range of applications to liquids and solids if water is transferred into a gas stream by controlled evaporation at low rates. The water detection system which is discussed in the following, namely WDS 400 by Sartorius, is very similar to this ﬁrst device; its major components are sketched in Fig. 1.24. The wet solid sample is put into an oven (see also Fig. 1.25b) which may be heated to a temperature of 400 C according to a pre-set temperature protocol. The oven is continuously swept by a dry inert or noble gas at a constant ﬂow rate of 100 ml min1 taking up the evaporated water (and possibly other volatile substances). The gas mixture ﬂows through a ceramic membrane that serves as a carrier for phosphorus pentoxide P2O5. Due to the extreme hygroscopicity of this substance, all water vapor is absorbed and phosphorus pentoxide is converted (in several hydration steps) to orthophosphoric acid P2 O5 þ 3H2 O ! 2H3 PO4

ð1:20Þ

1.4 Coulometry and Nuclear Magnetic Resonance

Fig. 1.25 Desktop coulometer (a) with oven (b) into which a powder sample is loaded (by courtesy of Sartorius Co.).

Gas components other than water will pass through the membrane without reaction. Voltage is applied to the membrane by two electrodes (printed on its surface) to dissociate the phosphoric acids, the ﬁnal step of the respective anodic and cathodic reactions being 4PO 3 ! 2P2 O5 þ O2 þ 4e

4H þ þ 4e ! 2H2

ð1:21Þ

Figure 1.26 shows the electrodes on the membrane which have a strongly interlaced geometry to get a large active area and short paths for the electrolytic reaction. The electric current through the electrolytic cell is measured as a function of time; integration yields the total electric charge consumed by electrolysis, which may be directly converted into a mass of water. Since hydrolysis and electrolytic recovery of phosphorus pentoxide are simultaneous reactions, care must be taken that the cell does not get saturated with water. To this purpose, a maximum electrolytic current (for the given device 100 mA) must not be exceeded, that is

Fig. 1.26 Electrolytic cell with magnification of the two interlaced electrodes (light gray) that are printed on the membrane (dark gray) (by courtesy of Sartorius Co.).

j29

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

30

water vapor must not be produced in the oven at too high rates (at a maximum 9.3 mg s1). On the other hand, too low electrolytic currents – associated with too low evaporation rates – will be measured with a higher relative error so that water content is obtained at lower precision (integration over time has no effect on the error). In conclusion, best results are obtained for elevated but not too high evaporation rates (here several mg s1). It should be noted that the value of the electrolytic voltage is not critical as long as it is well above 2 V, which is the decomposition voltage of water (Keidel, 1959). The efﬁciency of the cell depends on impurities and is regularly assessed by calibration measurements with a well-deﬁned amount of water. Since free water would evaporate too rapidly and lead to an overload of the detector, a standard substance, sodium wolframate containing crystalline water (Na2WO42H2O), is used; typically, 20–25 mg of standard substance (with 1.07% water) are used. If the efﬁciency is too low, the electrolytic cell has to be refreshed by cleaning with water and coating with an acetone solution of 85% orthophosphoric acid (H3PO4). Before performing the next analysis measurement, the cell must be dried and the acid converted into phosphorus pentoxide by electrolysis. The dehydration will, however, not be complete (HPO3 is considered the prevailing component) since the cell becomes an insulator with increasing concentrations of P2O5 (Keidel, 1959). For quantitative analysis of water in solid samples, the following procedure is applied: 1. 2. 3. 4.

Open the oven door and insert the sample scoop Close the oven door (a short time interval later) Heat the oven according to a pre-set temperature protocol Measure and integrate the electrolysis current over a given time interval.

It is obvious that such a measurement will not only detect the water from the sample, but also residual moisture in the ﬂow of carrier gas and moisture that enters the system when opening the oven door; (recall that saturated air at 20 C contains 17.3 mg ml1 water vapor and the total oven volume is 26 ml). From this, it is obvious that tare measurements without a solid sample are of paramount importance if small solids moisture contents are to be quantiﬁed. Such a tare measurement has to be done directly before quantitative analysis to account for changes of relative humidity in ambient air; furthermore, exactly the same procedure has to be respected as in the subsequent analytic measurements, that is same open time of oven, same temperature protocol and measurement duration. We will now return to our task of characterizing particles from a ﬂuidized bed dryer with respect to their moisture content, which corresponds to measuring water amounts in the range 100–2500 mg. Recalling that the temperature protocol ideally has to be chosen so as to evaporate water from the sample at a rate of several mg s1, we will apply two different protocols. The ﬁrst, which is applied to particles with rather low moisture, accomplishes a temperature increase to 130 C in one step and in total takes 10 min (see Fig. 1.27a). The second is intended for larger amounts of water; in order to prevent too high release rates, an intermediate temperature of 60 C is ﬁrst assumed before heating to 130 C in a second step; overall measurement duration is

14 min (see Fig. 1.28a). To obtain reproducible results, argon (99.998 vol.%) at a ﬂow rate of approximately 100 ml min1 is used as a dry carrier gas in all measurements. Tare measurements of electrolysis current for the two chosen temperature protocols are given in Fig. 1.29. One may assume a constant background level that originates from residual moisture in argon (a gas ﬂow of 100 ml min1 with 0.002 vol.% water vapor corresponds to a vapor ﬂow of 1.48 mg min1 or an electric current of 0.26 mA). The different durations of the two protocols result in different contributions from argon to the total detected moisture (14.8 and 20.7 mg for protocols 1 and 2, respectively). The signal above this background results from the moisture entering the oven during (sample) loading. Its shape depends slightly on the chosen temperature protocol but not its integral value (39.8 and 39.5 mg for protocols 1 and 2, respectively). In this light, we may understand the detection limit of the device that is given as 1 mg. In the following, ﬁve samples (A–E) with increasing moisture content are characterized. The complete measurement results are given for the driest and for the wettest sample in Figs. 1.27 and 1.28, respectively. In Figs. 1.27a and 1.28a the oven temperature is plotted along with the value set by the protocol. Figures 1.27b and 1.28b show the electrolysis current which is corrected by the tare measurement.

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

32

Fig. 1.29 Tare measurements for the two temperature protocols shown in Figs. 1.27 and 1.28; the converted electric charge is equivalent to 54.6 mg (protocol 1) and 60.2 mg (protocol 2) of water.

Figure 1.30 summarizes the corrected electrolysis currents and computed water amounts for all ﬁve samples. Having seen that the coulometric method can produce quantitative results of the desired high quality, we conclude our description by recalling its major advantages and disadvantages. The major advantages may be listed as: .

In the coulometric method, water is clearly distinguished by a chemical reaction, whereas in gravimetric methods, for example the magnetic suspension balance, weight loss during heating is recorded and the assumption must be made that water loss is the only reason for the weight change. In reality, however, elevated temperatures may also lead to weight loss by chemical reactions in the solid or evaporation of volatile substances.

.

The mass of water Mw is measured directly so that only the wet sample Ms,wet (original state) needs to be weighed to obtain the moisture content from X ¼ Mw/ (Ms,wet Mw). In gravimetric methods, the dry solid mass Ms,dry must also be

Fig. 1.30 Electrolysis current for five particles spanning a wide range of moisture content.

1.4 Coulometry and Nuclear Magnetic Resonance

measured to compute the moisture content as X ¼ (Ms,wet Ms,dry)/Ms,dry. This brings the problem of removing all water without any other changes to the sample. Furthermore, in the case of low moisture contents, the weight difference Ms,wet Ms,dry cannot be measured accurately due to limited balance precision, and this may reﬂect in a large error in X. .

The coulometric method may also be used for a rough quantitative distinction of surface water, capillary water and the more tightly bound water of crystallization if the temperature rise is performed in appropriate steps. The major disadvantages of the coulometric method are:

.

The sample as deﬁned by a porous structure containing a certain amount of water is destroyed so that the measurement cannot be repeated.

.

Sample water content and release behavior of the water must be known approximately so as to choose the optimal temperature protocol: on the one hand, the electrolytic cell must not get saturated; on the other hand, the release rate should not be too low so as to keep the measurement period short (see above). When looking at the stochastic behavior of particles in a continuous ﬂuidized bed dryer, such information is not available!

.

The measurement of one sample takes a relatively long time (about 20 min). If many samples need to be measured to describe stochastic behavior, this is a severe drawback.

.

The humidity of a relatively big gas volume (oven) needs to be corrected in a tare measurement.

1.4.5 Nuclear Magnetic Resonance

An alternative method to measure the amount of water contained in a wet sample uses the magnetic spin of its hydrogen nuclei 1H (protons, compare with Chapter 4). If protons are put in a magnetic ﬁeld, their magnetic moments will behave according to quantum mechanical rules and take one of two stationary states: parallel or antiparallel to the external magnetic ﬁeld B0. The parallel state is thermodynamically favorable so that a macroscopic magnetization M is observed, which is proportional to the number of protons; it increases with magnetic ﬁeld strength and decreases with temperature according to Boltzmanns law. In the unperturbed state, magnetization M stays aligned with the magnetic ﬁeld B0. However, if the two are not parallel, magnetization will rotate around the magnetic ﬁeld vector with nuclear magnetic resonance frequency v0, as shown in Fig. 1.31, and produce an electromagnetic signal that can be measured. The NMR frequency depends on the nucleus and on the magnetic ﬁeld B0; for protons, a magnetic ﬁeld of 7Tproduces a frequency of about 300 MHz. In order to get the magnetization vector M tilted with respect to B0, a small additional magnetic ﬁeld B1 is applied which rotates in the x–y-plane with NMR

j33

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

34

Fig. 1.31 Precession of magnetization M in an external magnetic field B0.

frequency v0. By adjusting the magnitude of B1 and the pulse duration, the ﬂipping angle can be tuned to 90 , which will produce the highest resonance signal. In practice, the same electromagnetic coil ﬁrst produces the rotating B1-ﬁeld and then (after a short dead time) measures the signal of the rotating M-vector. This NMR signal decays with the so-called transverse relaxation time T2 because the rotating protons get out of phase due to small variations of NMR frequency in time and space; in consequence, the component of M orthogonal to the z-axis becomes zero. On a longer time scale (characterized by longitudinal relaxation time T1), the magnetization will relax back to its equilibrium state, that is parallel to B0. This type of NMR measurement is referred to as free induction decay (FID) because the protons may relax after the initial pulse without further perturbation. The initial magnitude of the FID signal is proportional to the number of protons. However, the signal of adsorbed water decays faster than that of free water because of its strong interaction with the solid (Metzger et al., 2005). This is one reason why the overall signal does not decay exponentially. Experiments on the wet g-Al2O3 samples were performed in a Bruker Avance 300 MHz NMR spectrometer (see Fig. 1.32) with micro-imaging option. The sample was put in an NMR glass tube and set into the 5 mm resonance coil in a central position (see Fig. 1.33a). To insert the glass tube into the narrow opening, a conical Teﬂon guide was put on top of the resonance coil (see Fig. 1.33b). Free induction signals are plotted in arbitrary units in Fig. 1.34 for the ﬁve samples that have also been characterized by coulometry (see above). Additionally, the NMR signal for an empty tube (i.e. without sample) is shown as a dashed line. For good signal-to-noise ratio, 100 scans were added together with a time delay of 1 s to assure longitudinal relaxation. The magniﬁcation of the very ﬁrst data points (Fig. 1.34a) shows an initial contribution to the signal that is independent of the sample (dashed line) and decays in about 40 ms; it probably results from the resonance coil itself. The semi-logarithmic plot of the NMR signal (Fig. 1.34b) conﬁrms shorter decay times for relatively dry samples where adsorbed water is dominant; it also reveals that decay is not strictly exponential. On the basis of these ﬁndings it has been decided that the ﬁrst data points have to be discarded and that the initial signal amplitude is not estimated by an exponential

ﬁt but instead approximated by the ﬁrst reasonable value (measured after 34.5 ms). The reproducibility of these values was found to be around 1%. Summarizing the advantages of the described NMR method we may state that, in contrast to the method of coulometry: .

No approximate knowledge is needed about the moisture content of the sample because the same measurement protocol is applied to wet and dry samples.

.

The wet sample is not destroyed so the measurement may be repeated.

.

Experimental time can be made short, depending on the desired accuracy (100 s for the chosen protocol).

.

The measured particle moisture is affected by the gas in the test tube (about 2 cm3) only because of sampling – establishing new sorption equilibrium – and not because of the measurement method itself (cf. opening of oven door in coulometry). The resulting error may be reduced by ﬁlling the empty part of the tube with inert material.

j35

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

Fig. 1.34 Free induction decay for five samples and empty tube (a) first ten data points and (b) decay behavior over a longer period of time (semi-logarithmic plot).

1.4 Coulometry and Nuclear Magnetic Resonance

The major disadvantages of the proposed NMR method are: .

.

The need for calibration. Ideally, the signal is proportional to the mass of water Mw so that only one point would be required. Unfortunately, we will see that strict proportionality is not observed and that a calibration curve is needed instead. The high cost of the system, also in terms of operation and maintenance (especially the need for liquid helium and nitrogen to cool the superconducting magnet).

However, NMR devices can be found in all major research institutions because of their wide range of scientiﬁc applications. And the problem of calibration may be solved by combining the method with precise coulometric experiments. 1.4.6 Combination of Both Methods

In Figure 1.35, the NMR signals of the ﬁve selected samples are plotted versus the mass of water which has been measured (afterwards) by the method of coulometry. The non-zero signal of the empty tube is also shown. From the data points it becomes clear that one-point calibration (assuming proportionality) is not reasonable; furthermore, the comparison between linear and quadratic ﬁt reveals that the correlation is not strictly linear so that a quadratic calibration curve is chosen. Several additional data sets (not shown here) could conﬁrm the accuracy of the calibration curve. With this newly developed method, we will now measure distributions of particle moisture. 1.4.7 Experimental Moisture Distributions and Assessment of Model

The experiments for testing the model from Section 1.4.2 are carried out in a continuous laboratory scale dryer as depicted in Fig. 1.21, with a diameter of 150 mm

Fig. 1.35 Calibration of NMR signal by coulometry.

j37

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

and a batch size of approximately 3 l. The instrumentation provides various measurements of temperature, pressure, pressure difference, gas ﬂow rate, and inlet and outlet gas moisture. Three experiments were run with different particle ﬂow rates, but the same inlet solids moisture content (X0 ¼ 0.65 kg kg1), gas ﬂow rate (125 kg h1) and gas inlet temperature (80 C). The latter corresponds to an adiabatic saturation moisture content of Yas ¼ 22.3 g kg1. Additional process parameters are summarized in Tab. 1.8. In the model equations, the particle ﬂow rate N_ 0 and mean residence time t are affected. Furthermore, an increase in particle ﬂow rate increases the moisture load of the dryer, resulting in an increase in moisture content in the gas phase. Both effects cause a change in particle moisture content distribution and need to be considered. The presented analytical model contains the model parameter p to adjust the shape of the normalized drying curve to the respective material. As discussed in the previous sections, the drying curve needs to be derived from experimental data. In this study, such measurements were carried out in the magnetic suspension balance. Single particle drying was performed at a gas inlet temperature of 40 C, a gas inlet moisture content of 0.633 g kg1 and a pressure of 1022 mbar. For these conditions, the adiabatic saturation moisture content is 10.62 g kg1. The gas ﬂow rate was set to 100 ml min1, corresponding to a gas velocity of 3.6 mm s1. The drying curves for two different runs under the same process conditions are presented in Fig. 1.36.

One can see that the drying rate is approximately constant at 0.379 g s1 kg1 till a moisture content of about X ¼ 0.3. Assuming that this is the ﬁrst period drying rate, we can also calculate it from Eq. 1.15. The mass transfer coefﬁcient b can be determined from the Sherwood correlation of Eq. 1.59. For the given conditions the values, Sh ¼ 2.33 and b ¼ 0.038 m s1 are obtained with a Reynolds number of _ v;I ¼ 0:433 g s1 m2 is estimated from Eq. 1.15, Re ¼ 0.38. In turn, a drying rate of m which is somewhat higher than the measured value. This slight difference can have several reasons. First, the Sherwood number can be smaller than calculated due to non-ideal ﬂow conditions. Figure 1.37 shows that – instead of using the previously discussed basket or needle – the single particle was placed in a wire hoop. This may inhibit gas ﬂow and diffusion around the particle. For a Sherwood number of Sh ¼ 2 one would obtain an evaporation rate of _ v;I ¼ 0:372 g s1 m2 , which matches perfectly the experimental data. Another m explanation is the reduction of vapor pressure due to hygroscopicity of the material. This effect can be accounted for by modifying the normalization method and deﬁning the (then not constant) ﬁrst period drying rate as _ v;I ¼ rg b ðY eq ðX ; T p ÞY in Þ m

ð1:22Þ

Here, Yeq denotes the equilibrium moisture content resulting from the sorption isotherm X(w). The modiﬁed normalization concept has been extensively discussed by Burgschweiger et al. (1999) and applied successfully by subsequent authors (e.g. Burgschweiger and Tsotsas, 2002), but it is too complex for use with the present analytical model. Therefore, conventional normalization after van Meel (1958) is used here. In

this frame, a critical moisture content of Xcr ¼ 0.3 is read from the single particle data of Figure 1.36 and the evaporation rate of the ﬁrst drying period is determined from Eq. 1.15 with Sh ¼ 2. The equilibrium moisture content Xeq is derived from the sorption isotherm provided by Groenewold et al. (2000). In this way, the normalized data of Fig. 1.38 are obtained for the test material. To calculate moisture distributions for the dried solids from Eq. 1.16, one needs to ﬁt the drying curve according to Eq. 1.14 by adjusting the parameter p. The result of this ﬁtting is also depicted in Fig. 1.38. For dimensionless moisture contents F > 0.5 the ﬁtting does not represent the experimental data very well, due to the symmetric shape of the curve according to Eq. 1.14. This drawback is a natural price to be paid for applying an analytical solution that does not allow for an arbitrary functional approximation of the normalized drying curve. Anyway, it is sufﬁcient to justify the method, including its experimental background, as the ﬁnal results will show. Another crucial model parameter is K. According to Eq. 1.18, K depends on the diameter and density of the particle, the gas density and the adiabatic saturation moisture, which can all be either measured or calculated. Furthermore, it depends on the gas-side mass transfer coefﬁcient in the ﬂuidized bed. For this coefﬁcient several models have been suggested in the literature. In the present study we applied a Sherwood correlation recommended by Burgschweiger and Tsotsas (2002), where axial dispersion in the gas is considered in the kinetic coefﬁcient. Finally, K depends on the moisture content in the gas bulk, Y. To predict this moisture content, a model for the gas phase is required (ideal back-mixing, simple plug ﬂow or some more complicated model). However, and in order to keep the present approach analytical, the parameter K was determined simply by ﬁtting to the experimental results. In Tab. 1.8 the obtained values for Y and K are provided.

1.5 Acoustic Levitation

Fig. 1.39 Comparison of the experimental and calculated distributions of solids moisture at the outlet of a continuous fluidized bed dryer for different particle flow rates (parameters according to Tab. 1.8).

Distributions measured at different particle ﬂow rates and distributions calculated by Eq. 1.16 are plotted in Fig. 1.39. An increase in particle ﬂow rate leads to a decrease in residence time and, consequently, to higher solids moisture contents. For higher particle ﬂow rates (higher moisture loads) the gas moisture content Y increases (see also Tab. 1.8). Thus the relative humidity will increase, and the equilibrium state of the solids moves towards higher moisture contents. With the given set of parameters the experimental moisture distributions can be reproduced in a qualitatively satisfactory manner by the model. Deviations can be attributed to imperfect ﬁtting of the normalized drying curve by Eq. 1.14. An extended model, incorporating the mass and energy balances for the solid and gas phase, would provide better agreement between experiments and simulation. However, the respective solutions are more complicated and, thus, less instructive than the here presented simpliﬁcations.

1.5 Acoustic Levitation 1.5.1 Introductory Remarks

The free suspension of a small droplet or particle near a pressure node of a standing acoustic wave is called acoustic or ultrasonic levitation. The gravitational force acting on the sample is compensated by the sound pressure of the ultrasonic ﬁeld acting in a net upwards direction. The ﬁrst systematic description of acoustic levitation was published by King (1934). In the 1970s the American space agency became interested in this phenomenon as a tool for containerless processing under microgravity conditions. Currently acoustic levitation is applied to examine the

j41

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

42

drying behavior of suspended droplets and particles in the ﬁelds of chemistry, engineering and pharmacy. One central question when considering acoustic levitation is whether the sound pressure per se inﬂuences the drying behavior of a droplet or particle suspended in a standing wave? Although some work indicated that this inﬂuence may be negligible (Seaver et al., 1989; Tian and Apfel, 1996), more recent studies have demonstrated and provided a theoretical background for the perturbation of droplet drying rate by an acoustic ﬁeld (Yarin et al., 1999). The most recent advances in this technique include the application of IR-thermography to measure the droplet surface temperature proﬁle during drying (Tuckermann, 2002) and moisture detection in the exhaust gas stream using a dew point hygrometer (Groenewold et al., 2002), compare with Section 1.2.1. One new application is the determination of the drying kinetics of aqueous solutions of proteins and carbohydrates (Schiffter and Lee, 2007a, b). 1.5.2 Some Useful Definitions

An acoustic ﬁeld is characterized by its gas particle velocity and sound pressure. The gas particle velocity, B, is the velocity of a particle on a longitudinal pressure wave, given as the product of gas particle displacement, z, and angular frequency, v: B ¼ z v ¼ z 2pf

Bref is taken to be the lowest SVL detectable to the human ear, that is 5 108 m s1. The unit of SVL is the decibel (dB) which is therefore dimensionless. The sound pressure, Psound, is that of the root-mean-square pressure deviation caused by a sound wave passing through a ﬁxed point. It is the product of the medium density, r0, the speed of the sound wave, u0, and the gas particle velocity: Psound ¼ r0 u0 B

ð1:25Þ

Figure 1.40 illustrates how the sound pressure wave is p/2 out of phase to the gas particle displacement wave. The logarithmic ratio of Psound to a standardized reference sound pressure (Pref ¼ 2 105 N m2) is called the sound pressure level (SPL or Lp): Lp ¼ 20 log

Psound P ref

ð1:26Þ

1.5 Acoustic Levitation

Fig. 1.40 Shape of a horizontal sound pressure wave, Psound, and its associated gas particle displacement wave, z. Note that the Psound is p/2 out of phase with z.

1.5.3 Forces in a Standing Acoustic Wave

A standing acoustic wave is formed within a closed tube whose length, Lr, is an integral multiple of the half-wavelength, l/2, of the incident sound pressure wave: l Lr ¼ n ; 2

n ¼ 1; 2; 3; . . .

ð1:27Þ

The relation between the sound pressure waves frequency, f, and the tube length is given by: f ¼

u0 u0 ¼n ; l 2 Lr

n ¼ 1; 2; 3; . . .

ð1:28Þ

Interference of the incident and reﬂected sound pressure waves produces a series of nodes and anti-nodes in ﬁxed positions. The gas particle displacement, z, is zero at each node, and maximal at each anti-node, with the nodes and anti-nodes separated by a distance p/2. In an acoustic levitator (Fig. 1.41) a standing sound pressure wave is formed between an ultrasonic transducer at x ¼ 0 (e.g. a piezocrystal) which produces the incident wave, and a reﬂector placed at a distance Lr ¼ n l/2 (n ¼ 1, 2, 3, . . .). A particle or droplet can be suspended or levitated in the vicinity of one of the sound pressure nodes, where the sound pressure acting upwards on the surface of the particle or droplet is positive and balances the gravitational force acting downwards. King (1934) derived an expression for the sound pressure, Pa, exerted by a standing sound pressure wave in a gas of density r0, at the surface of a rigid particle of radius a, and density r1: Pa ¼ prC1 sinð2khÞ f ðaÞ

ð1:29Þ

j43

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

44

Fig. 1.41 Representation of incident standing sound pressure wave formed between transducer and reflector in an acoustic levitator. At the pressure nodes the gas particle displacement is 0, whilst that at the empty nodes is a maximum.

where C0 (in ms1) represents the constant of the solution applicable to the onedimensional wave equation, k is the wavenumber ¼ v/u0, h is the displacement of the center of the spherical particle from a node at h ¼ n p/k, a ¼ k a, and f (a) is given by: f ðaÞ ¼

The coefﬁcients Fn, Gn, and Hn are functions of a and can be expressed as polynomials of 1/a2 (given by King, 1934) together with: H2n ðaÞ ¼ F 2n ðaÞ þ G2n ðaÞ

ð1:31Þ

Equation 1.29 shows that the sound pressure acting on the particle in the standing wave is periodic and varies with the relative position of the center of the sphere to the nodes and anti-nodes. This behavior differs therefore from the sound pressure acting on a particle in a translating sound pressure wave, which is always positive.

1.5 Acoustic Levitation

Additionally, the sound pressure in the standing wave is much stronger than that in a translating wave. The standing sound pressure wave can therefore levitate a given droplet or particle, with its position relative to the nodes and anti-nodes depending on the waves amplitude and also on the particles radius and the relative density, r0/r1. The acoustic levitation of a deformable droplet – relevant for droplet drying studies – was analyzed by Yarin et al. (1998). A one-dimensional sound pressure wave is approximated by assuming an inﬁnite levitator with sound pressure: Psound ¼ A0e e

Fig. 1.42 Representation of incident standing acoustic wave taken from Yarin et al. (1998). (a) The positions of the nodes and antinodes in the sound pressure wave calculated from the numerical solution of Yarin et al. (1998). (b) The acoustic levitation force, FL, in dependence on both x and L, the distance between the center of the sphere and the adjacent anti-node. Note the region of positive acoustic levitation force.

j45

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

46

The effective amplitude, A0e, is selected to make Eq. 1.32 consistent with a levitator tube length of Lr, yielding: A0e ¼

A0 cosðvLr =u0 Þ

ð1:34Þ

A0 is the amplitude at the transducer surface, that is x ¼ 0. The approximated standing sound pressure wave described by Eqs. 1.32 and 1.34 gives node positions that are at most 5% removed from the exact solution for a levitator tube length of Lr (Yarin et al., 1998). This standing sound pressure wave is disturbed by the presence of a droplet levitated in the vicinity of one of the nodes, resulting in an additional scattered sound pressure wave: Pssound ¼ A0e eivt Ps ðrÞ

ð1:35Þ

where the dimensionless function Ps ðrÞ of the radius vector r is found from the Helmholtz equation: 2 v Ps ¼ 0 ð1:36Þ rPs þ u0 The total sound pressure existing at the spheres surface is now the sum of the sound pressures of the incident wave, Psound, plus the scattered wave, Pssound . Yarin et al. (1998) solved this problem by numerical evaluation of the associated boundary integral solutions to Eq. 1.36, and obtained the total sound pressure acting at the droplet surface, Pa. The resulting acoustic levitation force, FL, was then obtained by integrating Pa over the droplet from top to bottom. Their numerical result for FL in dependence on L could then be compared with the analytical result given for FL from Kings Eq. 1.29 in terms of L: A0e 2 sinð2a LÞ f ðaÞ ð1:37Þ F L ¼ pr0 a2 r 0 u0 where f(a) is as given in Eq. 1.30. The results in Tab. 1.9 illustrate the closeness of Yarins approximation to Kings analytical solution in Eq. 1.37. For a sound pressure wave of intermediate length (a ¼ 1) the acoustic levitation force is positive in the Tab. 1.9 A comparison of the one-dimensional acoustic levitation force, FL, existing along the standing sound pressure wave and acting on a sphere as calculated numerically by Yarin et al. (1998), and also from King (1934) analytical solution. FL is rendered dimensionless by dividing with r0 u20 a2 , and L by dividing with a;. A0e =r0 u20 ¼ 1:0, a ¼ 1.0, data taken from Yarin et al. (1998).

L

FL (Yarin et al.)

FL (King)

0 0.1 p/4 ¼ 0.785 1.0 p/2 ¼ 1.55

0.0096 0.2737 1.4148 1.2849 0.0466

0 0.2840 1.4294 1.2998 0.0594

1.5 Acoustic Levitation

range of L between 0 and p/2 (Fig. 1.42a), as predicted by Eq. 1.37. Furthermore, the maximum FL exists at L ¼ p/4. The numerical result differs from the analytical result by 1% (Yarin et al., 1998). For measurements with an acoustic levitator we must know at what sound pressure level acting at the spheres surface, SPLeff, the device is working. SPLeff is directly related to the effective amplitude of the standing sound pressure wave, A0e in dyne cm2 (Yarin et al., 1998): SPLeff ¼ 20 logðA0e Þ þ 74

Yarin et al. (1998) give two techniques for determining SPLeff in a levitator. First, the drop-out method that determines A0e by exploiting the balance of FL from Eq. 1.37 and gravity acting on the sphere, FG ¼ 4/3 pa3r1g, that exists when the sphere is levitated stably at some point between L ¼ 0 and p/2. A sphere is levitated within the standing acoustic wave at known driving voltage, U0, of the transducer. U0 is then reduced to the point U0m, where the sphere drops out of the wave because FL is now too small to compensate FG. At this drop-out point the effective amplitude, A0em, can be directly calculated from the properties of the levitated sphere: 1=2 4 a r1 r0 g u20 A0em ¼ ð1:40Þ f ðaÞ 3 Providing the amplitude of the transducer varies linearly with U0, then A0e can now be determined from: A0e ¼ A0em

U0 U 0m

ð1:41Þ

SPLeff is then directly available from Eq. 1.38 and is valid for the sphere size used in the experiment. The second technique calculates SPLeff from the aspect ratio (¼ horizontal radius (rh)/vertical radius (rv)) of a levitated droplet. As we shall see in Section 1.5.4.1, a droplet suspended in an acoustic ﬁeld will be deformed in shape by the asymmetric nature of the acoustic force acting on it. Yarin et al. (1998) used a numerical technique to solve the Bernoulli equation to give droplet shape as a function of Pa. By comparing measured aspect ratio with this solution the SPLeff can be calculated at any time during droplet drying. 1.5.4 Interactions of a Droplet with the Sound Pressure Field

A levitated droplet is inﬂuenced in its behavior by the standing sound pressure wave in four ways: 1. Deformation of the droplet, owing to anisotropic axial and radial levitation forces.

j47

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

48

2. Acoustic streaming ﬁeld near the surface of the levitated droplet which leads to acoustic convection and also solvent vapor accumulation, both of which phenomena greatly inﬂuence droplet drying rate. 3. Heating of the droplet, owing to oscillations of the ultrasonic transducer which change the temperature of the ambient drying air. 4. Increasing SPLeff during evaporation as the droplet size decreases. Any use of acoustic levitation to examine droplet or particle drying kinetics must recognize these effects. 1.5.4.1 Deformation of Droplet Shape A levitated droplet may deviate from a spherical shape because the sound pressure exerted by the standing wave is not uniform over the surface of the sphere. The extent of shape distortion depends on droplet size, the surface tension of the liquid, and the sound pressure (Trinh and Hsu, 1986; Marston et al., 1981). For example, a higher sound pressure/SPL produces greater distortion and therefore a higher aspect ratio at ﬁxed droplet size (Trinh and Hsu, 1986). The problem of predicting levitated droplet shape in dependence on sound pressure, Pa, was ﬁrst analyzed by Marston et al. (1981) for small deformations (Trinh and Hsu, 1986). Tian et al. (1993) extended this by including adjustment between the drop and its surrounding ﬁeld; the acoustic force that causes drop distortion is itself modiﬁed by the change in droplet shape. Yarin et al. (1998) adopted a numerical iteration technique to satisfy the equilibrium of FL and FG: bottom ð

2p

Pa

qr 4 rds ¼ pa3 r1 g qs 3

ð1:42Þ

top

where Pa is a function of droplet shape and L. Figure 1.43 reproduces a graphical comparison of experimental data of aspect ratio versus Psound taken from Trinh and Hsu (1986) with the predictions of Marston et al. (1981); Tian et al. (1993); Yarin et al. (1998). The deviation observed with Marstons prediction illustrates the importance of recognizing the coupling of droplet shape distortion with FL. Of particular interest is the distribution of Pa across the z-axis of the droplet surface shown in Fig. 1.44. At the top (z 0.5) and bottom (z 1.2) of the droplet it is Pa > 0 and the droplet surface is compressed. In the equatorial range (0.7 z 0.3) it is Pa < 0 and the droplet surface is stressed (Yarin et al., 1998). The result will be an oblate spheroid shape of the originally spherical droplet (Tian et al., 1993). 1.5.4.2 Primary and Secondary Acoustic Streaming The sound pressure ﬁeld around a droplet levitated in the standing wave results in streaming of the gas. The solution of the equations for an unsteady compressible boundary layer in the gas near the droplet surface gives the velocity of this acoustic streaming, huacoustici, as the time-average of multiple cycles of the standing acoustic

1.5 Acoustic Levitation

Fig. 1.43 Influence of sound pressure on the aspect ratio of droplets of silicone oil levitated in an acoustic levitator (a0 ¼ 450 mm, a ¼ 0.16). The filled squares show the original experimental data taken from Trinh and Hsu (1986). The three

curves represent the predictions given by Marston et al. (1981); Tian et al. (1993); Yarin, Paffenlehner and Tropea (1998). This figure has been redrawn from Yarin, Paffenlehner and Tropea (1998).

wave. The velocity ﬁeld is illustrated in Fig. 1.45 (Yarin et al., 1999) by the streamlines near the droplet surface. The distribution of huacoustici over the droplet surface is periodic, as seen in Fig. 1.46. In this representation x is the arc length of the droplet circumference measured from the bottom. The values of huacoustici given at x ¼ 0, x ¼ x2 and x ¼ x3 correspond to the points O1, O2 and O3 of the droplet surface shown

Fig. 1.44 The distribution of sound pressure, Pa, acting on the droplet surface along the z-axis calculated for a n-hexane droplet of a0 ¼ 1061 mm at a transducer voltage of 156 V. Note the periodicity of Pa across the axis of the droplet surface, with Pa > 0 at the top and bottom of the droplet. In the equatorial range Pa < 0. Figure reproduced from Yarin et al. (1998).

j49

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

50

Fig. 1.45 Sketch of the acoustic streaming field near a levitated droplet and the system of secondary toroidal vortices. The points O1, O2 and O3 refer to the calculated acoustic streaming velocities given in Fig. 1.46. This figure is taken from Yarin et al. (1999).

in Fig. 1.45. At the surface of the droplet a sound pressure boundary layer is thus formed by primary acoustic streaming. The radial thickness of this sound pressure boundary layer, d IAS, is given by Yarin et al. (1999) and Lee and Wong (1990): 1=2 2n0 dIAS ¼ ð1:43Þ v where n0 is the kinematic viscosity of the gas. For the example of a water droplet of diameter d ¼ 1.0 mm levitated in air (n0 ¼ 1.5 105 m2 s1) using a 56 kHz frequency transducer, dIAS ¼ 9.23 mm is obtained (Yarin et al., 1999). This is much smaller than the diffusional boundary layer around the levitated droplet calculated to be 92 mm; but as we shall see later, its inﬂuence on droplet evaporation rate can be substantial.

Fig. 1.46 (a) Sketches of a levitated droplet showing its coordinates, x: the arc length of the droplets circumference from the bottom point O1, y: the normal to x. (b) The distribution of uacoustic along the arc length, x, of the levitated droplet. The positions x ¼ 0, x ¼ x2 and x ¼ x3 represent the points O1, O2 and O3 in Fig. 1.45. Both graphs taken from Yarin et al. (1999).

1.5 Acoustic Levitation

Primary acoustic streaming results in an enhanced convection of solvent vapor away from the droplet surface. For a small spherical droplet where k 1, the solution for huacoustici reduces to (Yarin et al., 1999; Burdukov and Nakoryakov, 1965): huacoustic i ¼

45 B2 2x sin 32 v a a

ð1:44Þ

For a water droplet levitated at an SPLeff of 165.7 dB, Eq. 1.44 predicts a velocity of primary acoustic streaming of up to 0.93 m s1 along the arc length of the droplet circumference (cf. Fig. 1.46) (Yarin et al., 1999). This convective movement of the gas around the droplet must result in a Sherwood number, Sh > 2.0. Yarin et al. (1999) give the resulting distribution of the time-averaged Sh across the arc length x1 of the circumference of a small levitated droplet as: 1=2 45 B cos2 ðx 1 =aÞ ð1:45Þ hShi ¼ 2 4p ðvD10 Þ1=2 ½1 þ cos2 ðx1 =aÞ 1=2 The distribution of Sh is symmetrical about the vertical axis through point O3 in Fig. 1.45. The average Sh over the surface of the sphere is: hShi ¼ K acoustic

The quantity r ¼ a sin(x/a) is the r-coordinate of the droplet (cf. Fig. 1.46) that is set dimensionless with the initial droplet radius a0. The term uacoustic is set dimensionless with the gas particle velocity, B, and jhu acoustic ij r is averaged over the droplet surface. As droplet shape and hence r will change continuously during evaporation, Kacoustic has to be re-calculated continuously during the drying process. The Sh deduced from Eq. 1.46 will therefore be a time-function during droplet evaporation. For a small spherical droplet a good approximation of Sh is, however, given by: 1=2 45 B ð1:48Þ hShi ¼ 4p ðv D10 Þ1=2 This illustrates how, because of primary acoustic streaming, Sh depends directly on gas particle velocity, B, and hence on SPL via Eq. 1.25. These equations do not consider liquid ﬂow with the levitated droplet, which increases uacoustic by up to 10%. The corresponding increase in Sh is, however, negligible for mass transfer considerations (Rensink, 2004). The effects of secondary acoustic streaming on droplet evaporation rate are the opposite of that of primary acoustic streaming. Figure 1.45 illustrates that secondary

j51

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

52

acoustic streaming consists of a system of toroidal vortices around the levitated sphere. This system is caused by interaction of the primary acoustic streaming pattern with the walls of the levitator tube, or by droplet displacement from the pressure node. Secondary acoustic streaming has been veriﬁed experimentally (Trinh and Robey, 1994) and the mathematical problem solved (Lee and Wong, 1990; Yarin et al., 1999). In the vortices the solvent vapor from the evaporating droplet can accumulate. Kastner determined experimentally the large scale of the vortices (Kastner, 2001). For the example of ethanol the accumulation of solvent vapor in the vortices proceeded to saturation within 0.6 s for a 2 ml droplet evaporating at 25 C. This accumulation of solvent vapor in the vortices is predicted to decrease diffusional mass transfer from the droplet surface to the surrounding gas phase. To overcome the hindering effect of secondary acoustic streaming on droplet evaporation rate a forced ventilation gas stream needs to be introduced along the levitator axis. The accumulated solvent vapor is now removed from the vortices by forced convection (Seaver et al., 1989; Trinh and Robey, 1994). Yarin et al., (1997) visualized a ventilation gas stream passing around a levitated 5 ml n-hexadecane droplet inside an acoustic levitator at a SPLeff of approximately 156 dB. The images reproduced in Fig. 1.47 show how a ventilation gas stream of oriﬁce Reynolds number Re0 ¼ 70 moving up the levitator axis is trapped by the vortices of secondary streaming. Increase in Re0 up to 190 is sufﬁcient to prevent formation of the vortices, and the ventilation gas stream passes around the levitated droplet. According to Rensink (2004), the minimal ﬂow velocity of a ventilation gas stream necessary to neutralize the secondary acoustic streaming pattern by blow-out (uvent) is given by: uvent

Recall that A0 is the amplitude of the sound pressure wave at the transducer source surface (Eq. 1.34). For a water droplet levitated at a SPL of 165.7 dB the predicted uvent is 4.3 m s1. A ventilation gas velocity lower than uvent can, however, be sufﬁcient to prevent accumulation of solvent vapor in the toroidal vortices. This was shown to be true experimentally by Rensink (2004) for different solvent droplets. 1.5.4.3 Effects of Changing Droplet Size As elucidated in Section 1.5.4.1, a droplet levitated in a standing sound pressure wave is deformed to an oblate spheroid because the sound pressure acting on the droplet is not uniform along the sphere surface. During evaporation both the shape and the position of the droplet will, however, change. The droplet shape converges to that of a sphere (Kastner, 2001). The total pressure difference across the droplet surface comprises three parts (Tian et al., 1993):

Pi P o ¼ DPs þ DPG þ DP st

ð1:50Þ

where Pi and Po are the pressures at the surface approached from the inside or outside, respectively; DPs is the contribution from the sound pressure wave, DPG is induced by gravity, and DPst is the difference in uniform static pressure inside and outside the droplet. In the absence of a sound pressure wave DPst ¼ 2s=a

ð1:51Þ

where s is the surface tension of the liquid. Now, as the droplet shrinks during evaporation the decreasing radius of curvature will make DPst dominant over DPrad (Trinh and Hsu, 1986). The aspect ratio will therefore approach unity as the contribution from DPrad in Eq. 1.50 becomes less. Figure 1.48 shows experimental

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

54

data for evaporating water droplets. The decrease in k a at ﬁxed SPL causes the aspect ratio to decrease and approach unity. Simultaneously the displacement of the droplet center from the nearest pressure node, Dz, decreases because the evaporating droplet rises in the standing sound pressure wave within the range 0 < L < 2p (Yarin et al., 1999). This is caused by a decreasing resonance shift of the levitator as droplet size decreases. When the droplet is introduced into the standing sound pressure wave it will immediately be deformed into an oblate spheroid (see Section 1.5.4.1). This change in droplet shape alters the scattered sound pressure wave, shifts hereby the resonance of the levitator, and decreases the sound pressure acting on the droplet surface, Pa (Trinh and Hsu, 1986). During evaporation the droplet size decreases and hence the resonance shift induced by the droplet will be progressively ameliorated. The result is a continual increase in SPLeff, which returns to its unperturbed value when the droplet has disappeared. Figure 1.49 shows how the SPLeff increases with decreasing droplet size during evaporation (Yarin et al., 1998). The SPL needed to levitate the drop is directly proportional to the liquids density, r1. An increase in SPLeff means, however, a higher gas particle velocity, B, and hence increased Sh in Eq. 1.46. This occurs during droplet evaporation in a sound pressure ﬁeld and is expected to inﬂuence evaporation rate. The decrease in droplet size during drying and the resulting increase in SPLeff will raise FL and cause a rise of the levitated droplet in the standing wave. Furthermore, as the mass of the levitated droplet decreases, the balance of gravitational and levitation forces, FG and FL, dictates that the droplet rises in the standing wave: 4 A0e 2 sinð2a LÞ f ðaÞ ð1:52Þ p a3 r1 g ¼ pr0 a2 r 0 u0 3

Fig. 1.49 Increase in SPLeff as droplet volume decreases during evaporation for four solvents. The SPLeff was calculated from the change in the aspect ratio of the droplets during drying. Fig. taken from Yarin et al. (1998).

1.5 Acoustic Levitation

Fig. 1.50 Position of droplet within sound pressure wave is dependence on its mass. Dz is the distance between the center of mass of the droplet and the adjacent pressure node. The upper line shows how Dz changes with decreasing volume at constant density. The lower line shows the behavior as density decreases at constant volume. These data were taken from Kastner (2001).

As droplet mass (4/3 pa3r1) decreases because of solvent evaporation, the sine function must decrease proportionately and the droplet rises within the sound pressure wave. Figure 1.50 taken from Kastner (2001) illustrates the inﬂuence of loss of mass on Dz of a droplet according to Eq. 1.52. A decrease in droplet volume at constant droplet density has a much weaker effect on Dz than does a decrease in density at constant volume. In terms of drying of a solution droplet, the change in Dz is caused by progressive resonance amelioration and by decreasing droplet size till a solid porous particle has emerged (critical point). The subsequent change in Dz of the particle after the critical point is caused by change in density during solvent loss, since particle size now remains constant. This can be exploited to determine particle drying kinetics after the critical point (Yarin et al., 1999; Kastner et al., 2001). 1.5.5 Single Droplet Drying in an Acoustic Levitator 1.5.5.1 Drying Rate of a Spherical Solvent Droplet Mass transfer from an evaporating droplet suspended in a gas phase was also discussed in Chapter 5, Vol. 1 of this series, in the context of spray dryer simulation. In general, two approaches can be applied. The ﬁrst is to solve the conservation equations for a motionless sphere in an inﬁnite stagnant medium, and to employ an empirical correction factor to account for forced convection around the droplet (Frohn and Roth, 2000). The second is to use ﬁlm theory with analysis of the effects of forced convection on layer thicknesses for heat and mass transfer (Sirignano, 2000).

j55

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

56

The ﬁrst approach leads to the d2-law and is a steady-state, gas phase model at constant temperature. A single, spherical droplet of initial radius a0 and ﬁxed surface temperature, Tph, is suspended in a still gas phase of ﬁxed temperature T1. At the droplet surface the saturation vapor pressure of the liquid, p , exists, whilst in the gas phase there is a lower vapor pressure, p1. Solution of the one-dimensional diffusion _ v , yields (Frohn and Roth, 2000): equation for vapor ﬂow rate at the droplet surface, M ~ RTÞ ~ _ v ¼ 4p D10 aðtÞfp p1 g M=ð M

ð1:53Þ

~ is liquid molecular mass, where D10 is the diffusivity of the vapor in the gas phase, M ~ _ drop , is given and R is the universal gas constant. The rate of shrinkage of the sphere, M by: _ drop ¼ 4p r1 a2 ðtÞ da M dt

to yield for the time-proﬁle of a(t), otherwise known as the d2-law: a2 ðtÞ ¼ a20 b t

b¼

~ p 2D10 M p 1 ~ T ph T 1 r1 R

ð1:56Þ

ð1:57Þ

Droplet lifetime, tl, is then given by: tl ¼

~ ph T 1 Þ r1 a0 RðT ~ ph p1 Þ 2D10 MðP

ð1:58Þ

The d2-law is valid in still gas, but can be corrected in an empirical fashion to account for forced convection of the gas phase. A good approximation is that of Ranz and Marshall (1952) determined for a suspended solvent drop: Nu ¼ 2 þ 0:6 Re1=2 Pr 1=3 Sh ¼ 2 þ 0:6 Re1=2 Pr 1=3

The alternative approach to droplet drying kinetics according to Sirignano (2000) is based on ﬁlm theory to determine the radii, r, of the heat (index: t) and mass transfer (index: m) ﬁlms around an evaporating sphere in a moving gas phase (forced convection): r film;t ¼ a r film;m

Nu Nu 2

Sh ¼ a Sh 2

ð1:61Þ

Nu and Sh are the modiﬁed Nusselt and Sherwood numbers that account for the ﬁlm thinning effects of Stefan ﬂow: Nu ¼ 2 þ

d t,0 and dm,0 are the initial ﬁlm thicknesses at t ¼ 0. The result of Abramzon and Sirignano (1989) for the time-proﬁle of a(t) is analogous to Eq. 1.60: a2 ðtÞ ¼ a20 ðtÞbfilm t bfilm ¼

2 r0 D10 Sh lnð1BM Þ r1 2

ð1:64Þ

ð1:65Þ

Here BM ¼

yph y1 1yph

ð1:66Þ

is the Spalding transfer number that represents the driving force for vapor diffusion through a stagnant ﬁlm (Frohn and Roth, 2000). y is the mass fraction of solvent vapor in the gas. For a spherical droplet in an environment with no forced convection it is Sh ¼ 2.0, and Eq. 1.66 simpliﬁes to: bfilm ¼

2 r0 D10 lnð1BM Þ r1

ð1:67Þ

which is directly analogous to the d2-law. Again, these equations take no account of the inﬂuence of sound pressure ﬁeld on evaporation rate.

j57

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

58

1.5.5.2 Drying Rate of an Acoustically Levitated Solvent Droplet The problem of determining the effect of a sound pressure wave on the evaporation rate of a levitated droplet was tackled by Yarin et al. (1999). For a small sphere the average Sh over the sphere surface is a function of gas particle velocity, B, as given by Eq. 1.48. Since Sh is deﬁned as

hShi ¼

k 2a D10

ð1:68Þ

where k is the time-averaged mass transfer coefﬁcient at the droplet surface, it follows that k¼

Equations 1.71 and 1.73 are analogous to the d2-law Eqs. 1.56 and 1.57 with the inﬂuence of primary acoustic streaming, uacoustic, being accounted for. The droplet lifetime, tl, is given in this case by: tl ¼

~ ph T 1 Þ r1 a20 RðT ~ p1 Þ f45D10 =ð4pvÞg1=2 BMðp

ð1:74Þ

which is shorter than that predicted by the d2-law by the factor given by Eq. 1.48 for Sh. 1.5.5.3 Drying Rate of Droplets of Solutions or Suspensions The ﬁrst drying period of a droplet of a solution or suspension resembles that of a pure solvent droplet. It can therefore be described by the same equations, but taking into account the lowering of the vapor pressure by the dissolved substance. The

Ignoring the effect of the dissolved substance, a2 ðtÞ=a20 decreases linearly with time according to either Eq. 1.56 (d2-law), Eq. 1.64 by Abramzon and Sirignano or Eq. 1.71. After the critical point has been reached, the volume of the particle now existing should remain constant (Sherwood, 1929). Continued evaporation of solvent from the particle decreases both its mass and its density. As discussed in Section 1.5.4, this will cause the particle to rise (Dz decreases) within the ultrasonic ﬁeld to maintain the balance between FL and FG given by Eq. 1.52 at constant SPLeff. This particle movement can be used to determine the quantity of solvent evaporated in the second drying period, provided the SPLeff and hence A0e does not change after the critical point, and is known. The evaporation rate in this falling-rate drying period is then given directly from Eq. 1.37 (Yarin et al., 1999; Kastner et al., 2001): 2 A0e 2 _ fr ¼ pr0 a f ðaÞfsinð2aL1 Þsinð2aL2 Þg ð1:76Þ M Dt g r0 u0 determined from the droplet position at two times, L1 and L2, separated by Dt. Once _ fr is known, the mean particle density, rp, the mean moisture mass fraction of the M droplet, x1, and the mean particle porosity, e, can be calculated as time-functions (Kastner et al., 2001): M l ðtÞ þ M s Vp M l ðtÞ x 1 ðtÞ ¼ M l ðtÞ þ M s Ms eðtÞ ¼ 1 rs V p rp ðtÞ ¼

ð1:77Þ

Ultrasonic levitation is therefore one of the few techniques suitable for examining the drying process of a solution droplet during both drying periods. The _ fr ) and residual solvent mass fraction (x1) of a droplet/ _ cr or M evaporation rate (M particle can be determined at any desired point of time during evaporation. Furthermore, a droplet or particle can be removed from the levitation tube at any time for further analysis. 1.5.6 A Case Study: Single Droplet Drying of Water and an Aqueous Carbohydrate Solution

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

60

water and an aqueous solution of a carbohydrate useful in drug delivery (Schiffter and Lee, 2007a, b) illustrates the strengths and also the limitations of such experiments with an acoustic levitator. We present some selected results. 1.5.6.1 A Typical Acoustic Levitator A standard levitation system based on a published design (Yarin et al., 1999) is shown in Fig. 1.51. A 58 kHz levitator is ﬁxed within a plexiglas chamber, with the piezoelectric transducer in the roof and the reﬂector in its base. A drying gas is introduced into the levitator chamber through a hole in the center of the reﬂector, and is conditioned using a controlled evaporation mixer (CEM). A liquid ﬂow controller type L1-FAC-33-0 humidiﬁes the drying gas to 0.2–10.0 gwater h1. A gas ﬂow controller type F-201C-FAC adjusts the drying gas ﬂow rate to between 0 and 2.0 l min1. The drying gas temperature T1 is adjusted in the mixing unit W-202330-T to produce the conditioned drying gas stream. The image of a levitated droplet is recorded continually using a JAI CF-M4 2/3 monochrome CCD camera with bellows and a Nikon 60 mm macrolens 0.8 diameter frame connected to a PC via a PcDIG LVDS frame grabber (32 bit). Images are recorded and analyzed using Image Pro Plus software version 4.51 (Media Cybernetics).

Fig. 1.51 Design of an acoustic levitation system for measuring droplet drying kinetics and development of particle morphology. The plexiglas levitation chamber is covered by a plexiglas cover not shown in this illustration.

1.5 Acoustic Levitation

Fig. 1.52 Photographic sequence of droplet appearance during drying in the acoustic levitator. This droplet is of pure water of initial diameter approximately 500 mm drying at T1 ¼ 40 C in still air at an SPLeff of 162.47. The oblate spheroid shape of the droplet is evident from these photographs.

1.5.6.2 Evaporation Rates of Acoustically-Levitated Pure Water Droplets Figure 1.52 shows a typical sequence of droplet proﬁles obtained for pure water of a0 ﬃ 500 mm drying at T1 ¼ 40 C, 0% RH and a drying air ﬂow rate, uda, of 0 m s1. The SPLeff of 162.47 (at 20 C) required to levitate this droplet size results in the oblate spheroid shape evident in these photographs. From measurements of the vertical and horizontal diameters, dv and dh, a surface-equivalent radius is calculated and plotted in Fig. 1.53 as a2 ðtÞ=a20 versus evaporation time, t (labeled plot A). Figure 1.53 also contains the proﬁle predicted for water under these conditions using Eqs. 1.56 and 1.57 according to the d2-law (labeled plot B). For this calculation Tph was taken to be the adiabatic saturation temperature, Tas, p1 was taken to be zero (sink condition) and p was set to the value for the saturated water vapor pressure at Tas. The measured rate of evaporation (plot A) is clearly higher than that predicted by the d2-law (plot B). The deviation from the d2-law is quantiﬁed using Eq. 1.60 to calculate the Sherwood number at each time point of the experimental plots. The resulting temporal course of the ﬁtted Sh(t) is shown in Fig. 1.54 for three different T1, in which the maximum Sh(t) observed at T1 ¼ 40 C is 3.6, substantially larger than that of 2.0 for pure diffusion-controlled evaporation through a stagnant boundary-layer. This result clearly demonstrates the substantial inﬂuence of the sound pressure on the evaporation rate of droplets of this size over a wide temperature range. Figure 1.53 also contains the proﬁle calculated using Eq. 1.46 to account for the effects of primary acoustic streaming on Sh(t) (labeled plot C). Equation 1.46 also does not accurately predict the experimental data, since the measured evaporation rate (plot A) is now lower than that predicted (plot C). The evaporation rate determined in the levitator is higher than that predicted by the d2-law, but lower than that expected by considering the effects of huacoustici on mass transfer. This phenomenon can be attributed to the reduction in mass transfer caused by secondary

j61

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

62

Fig. 1.53 Evaporation of single droplets of pure water in an acoustic levitator. Plots of change in relative radius with evaporation time. A: Experimental result; B: prediction according to d2-law (Eqs. 1.56 and 1.57); C: prediction according to effects of primary acoustic streaming on Sherwood number (Eq. 1.46). The remaining plots are experimental results obtained using drying air ventilation at the flow rates uda.

acoustic streaming around the droplet. Rensink (2004) demonstrated how a forcedventilation gas stream ﬂowing axially through a levitator chamber can attenuate this phenomenon. Figure 1.53 contains the experimental plots of a2 ðtÞ=a20 versus t determined at two drying air ﬂow rates, uda, axially through the levitator chamber. Increasing uda causes a higher droplet evaporation rate than that measured in still air, that is uda ¼ 0. Clearly, the use of a forced-convection drying air stream will increase the evaporation rate under all conditions. In Fig. 1.53 it is, however, the attenuation of secondary acoustic streaming that causes the higher evaporation rate at uda ¼ 0.88 m s1. At this value of drying air ﬂow rate there is now good agreement

Fig. 1.54 The temporal variation of Sherwood number during single droplet drying at three different drying air temperatures. The Sherwood number was calculated by fitting Eq. 1.60 to the experimental data. Results taken from Schiffter and Lee (2007a, b).

1.5 Acoustic Levitation

Fig. 1.55 Measured and predicted values of Sherwood number for single droplet drying of pure water under conditions of drying air forced convection. The irregular plots are results obtained by fitting Eq. 1.60 to the experimentally determined values of droplet radius versus evaporation time. The straight lines are those predicted by Ranz and Marshalls correlation (Eq. 1.59). Data taken from Schiffter and Lee (2007a, b).

between the experimental plot and that predicted from Eq. 1.46 (plot C). According to Rensink (2004) this drying air ﬂow rate prevents the accumulation of water vapor in the levitator tube by destroying the vortices and hence neutralizes the retarding effect of secondary acoustic streaming on the droplet evaporation rate. If uda is higher than that necessary to neutralize secondary acoustic steaming, then a further increase in evaporation rate is observed (Fig. 1.53 for the example uda ¼ 2.21 m s1). This additional, convection-driven evaporation can most conveniently be analyzed using Ranz and Marshalls correlation between Sh and uda (Eq. 1.59). Figure 1.55 illustrates the example of uda ¼ 1.77 m s1 at T1 ¼ 40 C and uda ¼ 1.7 m1 s at 25 C. Reasonable agreement is obtained between the measured proﬁles of Sh(t) calculated by ﬁtting Eq. 1.60 to the a(t)-proﬁle and that predicted by Eq. 1.59. The experimental results are, however, only predicted accurately by Ranz-Marshall when uda is higher than that value found necessary to neutralize secondary acoustic streaming. With lower values of udaEq. 1.59 is inaccurate, because the drying air stream in this ﬂow range contributes to neutralizing an accumulation of solvent vapor within the vortices. 1.5.6.3 Evaporation Rates and Particle Formation with Aqueous Mannitol Solution Droplets The sequence of photographs in Fig. 1.56 shows the drying of a single droplet of a 10 wt% aqueous solution of mannitol. The position of the critical point and subsequent particle formation can be seen. Figure 1.57 shows a2 ðtÞ=a20 versus t for this system dried at T1 ¼ 60 C and 0% RH in still air. The plot is initially slightly concave to the x-axis up to a clear break at the critical point of drying tcp. The droplets aspect ratio decreases linearly up to the critical point, as DPst becomes more dominant in

j63

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

64

Fig. 1.56 Sequence of photographs of drying of a single droplet of a 10 wt% aqueous solution of mannitol at T1 ¼ 60 C. Note the oblate spheroid shape of the droplet and also the identifiable position of the critical point.

Eq. 1.50 with decreasing droplet size causing the droplet shape to converge to a sphere. At the critical point there is a sudden increase in aspect ratio which coincides with incipient formation of solid at the droplet surface. The critical point is thus clearly identiﬁable from the sharp changes occurring in both a2 ðtÞ=a20 and the aspect ratio.

Fig. 1.57 Results from single droplet drying of a 10 wt% aqueous solution of mannitol at T1 ¼ 60 C. The plot of relative droplet/ particle radius versus evaporation time shows a clear break point at the critical point. Also shown are the values for horizontal and vertical droplet/particle diameter, dv and dh. Data taken from Schiffter and Lee (2007b).

1.5 Acoustic Levitation

Fig. 1.58 Evaporation rate profiles for the single droplets of aqueous mannitol solution in dependence on the relative humidity of the drying air at T1 ¼ 60 C.

_ cr , is readily calculated from The droplet evaporation rate up to the critical point, M _ Eq. 1.75 and that after the critical point, M fr , from Eq. 1.76. In our experience Dz for use in Eq. 1.76 can be subject to substantial, erratic scatter. Indeed, Yarin et al. (1998) note that this parameter is highly sensitive, for example to horizontal displacements of the droplet in the standing sound pressure wave. The evaporation rate proﬁles given in Fig. 1.58 show the inﬂuence of RH at T1 ¼ 60 C in still air. A clear distinction between the initial constant-rate and subsequent falling-rate periods is evident, with the position of the critical point _ cr can be predicted from boundary-layer being clearly identiﬁable. The value of M theory. For a spherical solution droplet evaporating in still drying air at constant temperature (Charlesworth and Marshall, 1960): _ cr ¼ 2plda dDT=Dhv M

ð1:78Þ

where lda is the thermal conductivity of the drying air at the droplet surface temperature, d is the mean average droplet diameter between t ¼ 0 and tcp, DT is the difference between the temperature of drying air, T1, and the droplet surface temperature given by the adiabatic saturation temperature, Tas, and Dhv is the enthalpy of evaporation of water. The evaporation time up to the critical point, tcp, is then given by Schiffter and Lee (2007a, b): _ cr tcp ¼ DM w;cr =M

ð1:79Þ

where DMw,cr is the total mass of water lost between t ¼ 0 and tcp. This is given by 4/3 p (a30 a3cr )rpxw, with acr being the droplet/particle radius at the critical point and xw the weight fraction of water in the solution. _ cr are some three The results in Tab. 1.10 show that the measured values for M times larger than those predicted by Eq. 1.78. Consequently, the measured values for tcp are much smaller than those predicted by Eq. 1.79. These discrepancies are a

j65

j 1 Measurement of Average Moisture Content and Drying Kinetics for Single Particles, Droplets and Dryers

consequence of the effect of huacoustici around the levitated droplet, as we have already seen in Section 1.5.6.2 with pure water. It is likely that these discrepancies between measured and predicted evaporation rates will depend on the initial SPLeff required to levitate a particular droplet size. Tian and Apfel (1996) found, for example, no inﬂuence of a sound pressure ﬁeld of low SPL of <150 dB on droplet evaporation rate and obtained a good agreement with Eqs. 1.56 and 1.57. _ cr results in a decrease in the quotient of the dried particle to initial Lower M droplet radii, ap/a0 (Tab. 1.10), at the same solids content. Since a(t) changes only marginally after the critical point, the value of ap/a0 represents that size at which the precipitating mannitol forms a mechanically-stable crust at the droplet surface. The _ cr is reduced. If the droplet dries time to this point is shifted to longer values when M p ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 3 to a solid particle then ap =a0 ¼ rm;0 =rs , where rs is the true density of the solid. A solid, fully-crystalline particle would fully dry to ap/a0 ¼ 0.405. The measured values in Tab. 1.10 are all substantially higher than this theoretical result and give a quantitative measure of degree of particle porosity or hollowness. The drying behavior of the mannitol solution droplets is thus characterized by a sharp critical point caused by crystallization from a super-saturated surface solution, followed by a rapid decline in evaporation rate as moisture must now penetrate through the permeable crystalline crust.

With the help of examples, we have shown how these techniques can be used to: . . . . .

measure single particle drying kinetics determine kinetics of single drying droplets measure the distribution of moisture in a population of particles monitor the change of solids moisture content in convective dryers derive drying curves for the entire hold-up of dryers that can be scaled-down to single particle kinetics if an appropriate model is available.

What the discussed experimental techniques do not provide is resolution of the spatial distribution of moisture in drying solids. Methods capable of delivering this information are the subject of Chapters 2–4. Additional Notation Used in Chapter 1

Moisture distribution inside food products affects their quality, processing characteristics, drying efﬁciency and so on. Therefore, it is an important factor to be measured; there is not only an academic but also an industrial need for methods for the measurement of moisture distribution inside food products. Magnetic resonance imaging (MRI, see Chapter 3) is one of the possible methods. Several studies of the visualization of moisture distribution inside foods have been reported (Irie et al., 2004; Ramos-Cabrer et al., 2006). One of the advantages of the MRI technique is that it allows the internal structure of a sample to be measured non-destructively. However, expensive instruments and high maintenance cost are involved. In addition, only liquid water and related molecules can be measured and even ice cannot be easily detected by MRI. On the other hand, near-infrared (NIR) spectroscopy has been widely used for moisture content measurement. However, moisture distribution inside food is rarely measured in this way because every part of the food cannot be measured by the single point detector used in NIR spectroscopy. To overcome this limitation of NIR spectroscopy, NIR spectral imaging has been studied as an extension of NIR spectroscopy from single point detection to two- or three-dimensional measurement. Quantitative analysis of constituents and visualization of their distributions can be carried out concurrently by NIR spectral imaging. Visualization of sugar distribution in fruits (Martinsen and Schaare, 1998; Sugiyama, 1999; Tsuta et al., 2002), anthocyanin in vegetables (Nagata et al., 2006; Kobayashi et al., 2006) and detection of foreign substances in fruit material (Tsuta et al., 2006) can be listed as examples of NIR spectral imaging. Devices required for NIR spectral imaging are relatively inexpensive compared to those for MRI and several different constituents including water and ice can be visualized at the same time. Therefore NIR spectral imaging can be applied for visualization of moisture distribution even where MRI cannot be used.

NIR spectroscopy (Iwamoto et al., 1994) is a spectroscopic method utilizing the NIR region of light. The constituents of a sample can be quantitatively or qualitatively analyzed by illuminating the sample and observing the absorption spectra, which reﬂect absorption of light by each constituent within speciﬁc wavelength ranges. NIR spectroscopy is based on molecular overtone and combination vibrations. Such transitions are forbidden by the selection rules of quantum mechanics. As a result, absorption of light in the NIR region is typically quite small and light can penetrate much farther into a sample than in the mid-infrared region. NIR spectroscopy is therefore not a particularly sensitive technique but it can be very useful in probing the bulk material with little or no sample preparation. NIR spectroscopy has been studied since the 1940s, but began to receive much attention in the 1960s when quantitative analysis of the moisture content of fruits (Norris and Butler, 1961) and grains (Ben-Gera and Norris, 1968) by NIR spectroscopy was reported. In the 1970s Hunt et al. (1977) developed a quantitative analytical method for protein in grains, which was much easier and faster than the conventional chemical analysis method and was thus adopted as an ofﬁcial method by the Canadian Grain Commission, the United States Federal Grain Inspection Service and so on. NIR spectroscopy therefore became highly regarded and its application expanded drastically along with improvement in accuracy by innovations in instrumentation, progress in the computer ﬁeld and development of modern statistical analysis methods in the 1980s. Nowadays, it is widely adopted as an easy and fast measurement method, replacing conventional chemical analysis in the food industry, the chemical industry, medical technology and so on. 2.2.2 Lambert–Beer Law

Suppose we have a sample of thickness d that contains a constituent with concentration c, as shown in Fig. 2.1. When light of wavelength l with an intensity of I0(l) illuminates the sample its intensity declines to It(l) as it passes through the sample. The absorbance, which is the extent of absorption of light by the constituent, can be calculated from the relationship AðlÞ ¼ log ðI t ðlÞ=I0 ðlÞÞ

The absorbance spectrum shown in Fig. 2.2 can be acquired by using a spectrometer to measure the absorbance at each wavelength. In this ﬁgure, a higher absorbance value indicates that light is absorbed more strongly, and it can be seen that light is strongly absorbed at 444, 676 and 978 nm. Supposing that there is no reﬂection, scattering and ﬂuorescence except for absorption of light within the sample, the relationship between A(l), d and c can be described by AðlÞ ¼ cde

ð2:2Þ

Here, e is a constant called the absorption coefﬁcient. Equation 2.2 is called the Lambert–Beer law. It indicates that the absorbance is proportional to the constituent concentration and the thickness of the sample. This law is virtually applicable also in the case of diffuse reﬂection measurement by illuminating the sample and measuring the intensity of reﬂected light, as shown in Fig. 2.3. If there are multiple Fig. 2.3 Diffuse reflection measurement.

constituents in the sample, the total light absorption by the sample is the sum of the absorbance of each constituent: AðlÞ ¼

n X

ci dei

ð2:3Þ

i¼1

This equation, on which NIR spectroscopy is based, indicates that the concentration of each constituent can be calculated by measuring only the total absorbance of the sample at the absorption band of every constituent. Practically, it is difﬁcult to measure I0(l) directly in order to calculate A(l), especially in the case of a diffuse reﬂection measurement. Therefore, a white reference board made of material without any speciﬁc absorption band in the NIR region is utilized as a standard in order to calculate the apparent absorbance A0 ðlÞ ¼ log ðI t ðlÞ=I s ðlÞÞ

Here, A(l) and As(l) are real absorbance values of the sample and white reference board. Equation 2.5 shows that the apparent absorbance is acquired by subtracting As(l) from A(l). Since As(l) is constant regardless of constituent concentrations, linearity of Eq. 2.3 is maintained when A(l) is replaced by A0 (l). Because the apparent absorbance is usually measured in actual experiments, apparent absorbance is often called simply absorbance. In the practical application of NIR spectroscopy, calibration curves, from which constituent concentrations can be calculated from absorbance, are developed by measuring the absorbance spectra of samples with known constituent concentrations and calculating the product of dei of Eq. 2.3 for each constituent by statistical methods. Using these calibration curves, the constituent concentrations of unknown samples can be determined by measuring only the total absorbance. NIR spectroscopy therefore is a much easier and faster method than conventional chemical analysis. 2.2.3 Hyperspectrum

NIR spectral imaging is an extension of NIR spectroscopy from single point detection to two- or three-dimensional measurement. The spectrum is measured at one single

2.2 Principles of Near-Infrared Spectral Imaging

Fig. 2.4 Hyperspectrum.

point of the sample in conventional NIR spectroscopy, while one spectrum is acquired at every point of a surface of the sample in NIR spectral imaging. For example, when using a one-mega-pixel digital camera to acquire spectra of the surface area, the data volume is one million times larger than that measured by the conventional method. A series of data acquired during NIR spectral imaging is called a hyperspectrum and contains not only optical information from the sample, as in the case of the conventional method, but also spatial information, as shown in Fig. 2.4. Acquisition and analysis of a hyperspectrum enable quantitative analysis of a constituent and visualization of its distribution at the same time, which is a strong advantage of NIR spectral imaging. There are various techniques for acquisition of spectral and spatial information in NIR spectral imaging. The appropriate technique for the research objective should be selected by considering their characteristics. NIR spectral imaging will be classiﬁed by the type of spectral and spatial information acquisition techniques in the following two sections. 2.2.4 Classification by Spectral Information Acquisition Technique

The spectral information contained in a hyperspectrum can be acquired by placing a device working as a spectrometer in front of an illuminator or detector. The major devices used for spectral information acquisition are listed in Tab. 2.1. A bandpass ﬁlter is a device that lets light within a certain range of wavelength pass and rejects any other light. It is inexpensive and has high transmittance, which makes the data acquisition time shorter. However, the acquisition of sequential spectra is

difﬁcult because multiple ﬁlters are necessary for data acquisition at different wavelengths. A grating is an optical device consisting of a surface with many parallel grooves that disperses a beam of light into its constituent wavelengths to produce its spectrum. It is commonly used in conventional NIR spectroscopy and sequential spectra can be easily acquired with it. The light intensity, however, is drastically attenuated by a slit placed in front of the grating so that it takes a long time to acquire the whole hyperspectrum. A tunable ﬁlter combines the high transmittance of a bandpass ﬁlter with the variability of wavelength of a grating. A liquid crystal tunable ﬁlter (LCTF), which is a typical tunable ﬁlter, consists of electrically controlled liquid crystal elements and birefringence ﬁlters to select a speciﬁc wavelength of light for transmission through the ﬁlter with the exclusion of all others. The transmission wavelength of a LCTF can be switched from one to another within 50 ms so that sequential spectra can be easily acquired. In addition, a LCTF has high maintainability because it has no moving parts. It is, however, much more expensive than a bandpass ﬁlter or grating. An acoustic optical tunable ﬁlter (AOTF), which is another example of a tunable ﬁlter, utilizes the phenomenon that ultrasound propagating through an acoustic optical element has a diffracting function like a grating and has almost the same characteristics as a LCTF. 2.2.5 Classification by Spatial Information Acquisition Technique

The major spatial information acquisition techniques are listed in Tab. 2.2. X–Y scanning is a technique to measure the spectrum of a point of a sample by a single point detector. Spatial information can be acquired by moving the sample or the detector in the direction of the X and Yaxes, which is different from the conventional method. Spectra are measured under the same conditions and there would be no shading caused by sensitivity variations between detectors and/or lighting variations. On the other hand, it takes a long time to acquire a hyperspectrum because repetition of the measurement for as many times as the number of pixels of the image to be acquired is necessary.

Intermediate Intermediate Line sensor between above between above two two

Image acquisition is a technique to measure spatial information at once using an array of detectors aligned in a plane, such as a CCD array. Its advantage is quick data acquisition, while shading should be corrected in order to obtain proper data reﬂecting the optical characteristics of the sample. Line scanning, which is also called the pushbroom method (Mather, 1987), is a technique using an array of detectors, arranged in a line, to acquire a spectrum by means of combining the results from each detector during one measurement. Spatial information can be obtained by moving the sample or the detector in a direction perpendicular to the array. Line scanning is intermediate in characteristics between X–Y scanning and image acquisition; data with less shading than in the latter can be acquired in a shorter time than in the former.

A hyperspectrum is a three-dimensional data set that consists of two spatial coordinates and one spectral coordinate. It is difﬁcult to analyze the hyperspectrum as it is. Hence, spectral images, which are images of the sample taken at different wavelengths, are usually extracted from the hyperspectrum (Fig. 2.5b). Image processing and spectral analysis are then applied to these images. 2.3.2 Noise and Shading Correction

Acquired spectral images include (i) thermal noise due to dark current thermal electrons; (ii) bias signals to offset the detector slightly above zero A/D counts; (iii) sensitivity variations from pixel to pixel on the detector and (iv) lightingvariations on the

samples surface. The noise and shading corrections shown in Fig. 2.5c are applied to each spectral image to compensate for the above (SBIG, 1998; Morita et al., 1992; Fukushima, 1996). This can be expressed by the relationship Corrected image ¼ ðoriginal imagedark frameÞ=ðflat fielddark frameÞ ð2:6Þ In Eq. 2.6, the dark frame is the image acquired under the same conditions as the original image except for the absence of lighting. Subtracting it from the original image allows corrections for (i) thermal noise and (ii) bias signals. On the other hand, the ﬂat ﬁeld is obtained as a reference image by taking an exposure of a uniformly lit planar object such as a ceramic board. After the dark frame has been subtracted from the ﬂat ﬁeld in the same way as in the numerator, the ratio between the two images is obtained. This procedure compensates the effect of (iii) sensitivity variations and (iv) lighting variations. 2.3.3 Conversion into Absorbance Image

The numerator and the denominator of Eq. 2.6 correspond to the intensity of the sample and white reference board in NIR spectroscopy. Therefore, the absorbance

2.3 Image Processing

image can be acquired as shown in Fig. 2.5d, according to the scheme Absorbance image ¼ log ððoriginal imagedark frameÞ= ðflat fielddark frameÞÞ ¼ log ðcorrected imageÞ ð2:7Þ Each pixel of the image indicates one value of absorbance. 2.3.4 Acquisition and Pretreatment of Spectral Data

In order to utilize spectral information, boundaries composed of closed curves are set surrounding the areas to be analyzed in the absorbance images, as shown in Fig. 2.5e. These boundaries deﬁne so-called regions of interest (ROIs). When the average absorbance values of the pixels within the ROIs of the spectral images at each wavelength are calculated, absorbance spectra can be acquired, as shown in Fig. 2.5f. Pretreatment methods such as smoothing and the derivative method are often applied to the spectra to remove noise effects and spectral shifts between the samples. Among various spectral pretreatment methods, the second derivative method is especially important and most often used in NIR spectroscopy because of the following features and merits (Katsumoto et al., 2001): 1. Positive peaks in a raw spectrum are converted into negative peaks in a second derivative spectrum. 2. The resolution is enhanced, resulting in a better separation of overlapping peaks and greater emphasis of small peaks. 3. The additive and multiplicative baseline shifts in a raw spectrum are removed. By applying the truncated Taylor series expansion, a second derivative spectrum can be calculated as follows (Morimoto et al., 2001): f 2 ðxÞ ¼ ð f ðx þ DxÞ2f ðxÞ þ f ðxDxÞÞ=Dx 2

ð2:8Þ

Here, f (x) is the spectral function at x, and f 2(x) is the second derivative function at x. Actual spectral data, however, take discrete values because of the limited wavelength resolution of NIR spectrometers. Therefore, a second derivative spectrum is calculated in NIR spectroscopy as d2 Aðli Þ ¼ Aðli þ k Þ2 Aðli Þ þ Aðlik Þ

ð2:9Þ

Here, A(li) is the absorbance at li, d2A(li) is the second derivative absorbance at li, and k is the distance between the neighboring wavelengths, which is called a derivative gap. Equation 2.9 shows that absorbance values at three wavelengths of li þ k, li, and li–k are sufﬁcient to calculate the second derivative absorbance at li. When Eq. 2.9 is applied to the absorbance at each wavelength, a second derivative spectrum can be acquired. Equation 2.9 also indicates that a second derivative

absorbance image, where the value of each pixel expresses the second derivative of absorbance, can be obtained as 2Der: absorbance image at li ¼ absorbance image at li þ k 2 absorbance image at li þ absorbance image at lik :

ð2:10Þ

2.3.5 Analysis of Absorbance Spectra

The parts on which the ROIs are set are extracted from the sample for chemical analysis to measure the actual concentration of the target constituents. Statistical methods such as multiple linear regression or the partial least squares method are then applied to the acquired concentration data and the absorbance spectra of the ROIs to derive calibration curves for prediction of the concentration of an unknown sample, as shown in Fig. 2.5h. When chemical analysis of the speciﬁc parts of the sample is difﬁcult to conduct and no calibration curve can be obtained, absorbance spectra are examined to specify the absorption peaks of the target constituent. The magnitude of the peaks can be used for relative concentration images. 2.3.6 Visualization of Constituent Distribution

In general, a calibration curve utilized in NIR spectroscopy is a linear polynomial that contains several absorbance values at different wavelengths and can be written in the form c¼

n X

ai Aðli Þ þ b

ð2:11Þ

i¼1

Here, c is the concentration of the considered constituent, n is the number of wavelengths used in the calibration curve, A(li) is the absorbance at li, ai is the coefﬁcient of A(li) and b is a constant. In the same way, a constituent image, in which the value of each pixel indicates the concentration of the constituent, can be acquired by image arithmetic as Constituent image ¼

n X

ðai absorbance image at li Þ þ b

ð2:12Þ

i¼1

When a linear color or gray scale is applied to the constituent image, concentration of the constituent and its distribution can be visualized, as shown in Fig. 2.5j. If there is no calibration curve, then, by applying a linear color or gray scale to the absorbance image at the absorption peak of the target constituent, the relative concentration and distribution of the constituent can be visualized.

In the following sections, an application of NIR spectral imaging for determination of the absorption peaks of water and ice will be presented. Subsequently, visualization of moisture distribution inside soybean seeds utilizing the information from the absorption peaks of ice will be explained. 2.4.1 Specification of the Absorption Bands of Water and Ice 2.4.1.1 Imaging Apparatus The imaging apparatus utilized in this study is shown in Fig. 2.6. It was composed of a material cutting device called a Microslicer (AST-024s, Toshiba Machine Co., Ltd, Japan), a spectral illuminator and a NIR camera. The microslicer comprises a rotating microtome and a stepping motor. A sample is set in a sample holder above the motor and pushed up by the motor with a few micron increments. The increment can be adjusted from 1 to 30 mm with 1 mm accuracy. The top part of the sample is cut by the rotating microtome repeatedly so that cross sections at different depths are exposed serially. The sample holder can be maintained at about 15 C by an immersion cooler so that frozen samples can be measured. The spectral illuminator (S-10, Soma Optics Inc., Japan) comprises a xenon lamp box and a grating monochromater. It is connected to a germanium-doped light guide with a condensing lens (custom-made by Soma Optics Inc., Japan) and can illuminate the exposed surface of the sample at any wavelength from 400 to 1600 nm. The NIR camera (XEVA-USB-FP, XenICs, Belgium) is set on a ﬂuorescence microscope (BXFM, Olympus, Japan) with a ﬁve times objective lens for the NIR region (M Plan NIR 5 , Mitsutoyo Corp., Japan). The NIR camera has 320 256 pixels and its gradation is 12 bits (4096 steps). In addition, because its imaging sensor is made of an InGaAs array, it is sensitive in the wavelength region from 900 to 1600 nm, in which a normal CCD camera has little or no sensitivity. No ﬂuorescence

ﬁlter was installed in the microscope so that spectrometry by the spectral illuminator could work. 2.4.1.2 Acquisition of Hyperspectra of Water and Ice A white ceramic board, which was used as a ﬂat ﬁeld, was placed on the microslicer. Its images were taken by the NIR camera with changing wavelength of the spectral illuminator from 1400 to 1598 nm at 2 nm intervals with 12 ms exposure time. As a result, a hyperspectrum of 320 256 pixels 100 wavelengths was acquired. A pure water droplet with a volume of 1 ml was then added on a white ceramic board so that the droplet was in the view of the NIR camera. In the same way as for the white ceramic board, its hyperspectrum was acquired. After freezing the water droplet by using the cooler of the Microslicer, the hyperspectrum of the frozen droplet was obtained similarly. A dark frame was then taken with the lamp of the spectral illuminator switched off. 2.4.1.3 Spectral Analysis After noise/shading correction and conversion into absorbance images were carried out, an ROI was set surrounding the whole water droplet in the spectral images, as shown in Fig. 2.7. The average absorbance spectrum within the ROI was then calculated. This spectrum is depicted in Fig. 2.8. In the same way, the absorbance spectrum of the frozen droplet was acquired. In these working steps, image processing software (Image Pro Plus 5.0, Media Cybernetics Inc., USA) was utilized. Spreadsheet software (Excel 2003, Microsoft Corp., USA) was then used to calculate the second derivative absorbance spectra with a 20 nm gap and examine both the absorbance and the second derivative absorbance spectra. It was clariﬁed that the absorption peak of water was located at 1454 nm and that of ice at 1500 nm in the absorbance spectra. Furthermore, the negative absorbance peak of water was found to be at 1468 nm and that of ice at 1484 nm in the second derivative absorbance spectra (Fig. 2.9).

2.4.2.2 Acquisition of Hyperspectra The frozen samples of soybean seeds were placed in the microslicer to be cut. The cutting process was repeated until the hypocotyl and the embryo were exposed. The hyperspectra of the exposed surface were acquired by the NIR camera under the same conditions as for the droplet except for an exposure time of 50 ms. The hyperspectra of a white ceramic board and a dark frame were also acquired in the same way as in the case of the water droplet. 2.4.2.3 Spectral Analysis After noise/shading correction and conversion into absorbance images had been carried out, the ROIs were set on the periphery and center parts of the soybean seeds in the absorbance images, as shown in Fig. 2.10. The average absorbance and second derivative absorbance spectra were then calculated with a gap of 20 nm within the ROIs, as shown in Figs. 2.11 and 2.12. In the absorbance spectra of the periphery of all soybean seeds (except those of the original sample without water soaking), absorbance peaks were observed at around 1500 nm, where the absorption peaks of ice were also observed in the case of the frozen droplet. Because the water inside the seeds was frozen, it was considered that light absorption at 1500 nm indicated the presence of ice resulting from water penetration during the water soaking process. However, no speciﬁc trend related to water soaking time was found. On the other hand, it was observed that the second derivative absorbance at 1484 nm, where negative absorbance peaks were located in the case of the frozen droplet, became smaller with soaking time. This trend is stronger at the periphery than in the center of the samples. Therefore, it was considered to indicate that an increase in moisture content takes place during the water absorption process. Image processing and spreadsheet software, as in the case of water droplet, were utilized in these derivations.

2.4.2.4 Visualization of Moisture Distribution Second derivative absorbance images of the soybean seeds at 1484 nm were developed as shown in Fig. 2.13 by applying Eq. 2.10 to the absorbance images at 1464, 1484 and 1504 nm. In these images, pixels with a low value of second derivative absorbance spread from the periphery towards the center of the soybean seeds as the soaking time increased. Because a lower value of second derivative absorbance at

1484 nm indicates a larger moisture content, it may be concluded that water has penetrated deeper inside the sample seeds as the soaking time became longer, which is consistent with the water movement during the water soaking process. Therefore, these images seem to reﬂect the real moisture distribution in the samples.

2.5 Future Outlook

Not many applications of NIR spectral imaging for visualization of moisture distribution in foods have been reported yet and breakthroughs in various aspects can be expected. One possible progress would be the development of reliable calibration curves for the moisture content of small size foods such as grains and seeds. Utilization of a microtome to prepare cross-sections of a sample would be promising, because chemical analysis of a cross-section can be carried out after acquisition of its hyperspectrum. Accurate calibration curves can be developed from statistical analysis of several hundred hyperspectra and the actual moisture content data acquired by the chemical analysis. Three-dimensional visualization of moisture distribution inside foods can also be expected in the near future. It can be achieved by repetition of image acquisition at the absorbance peak of ice in combination with sample slicing by the microslicer. 3D visualization combined with a calibration curve covering a wide range of moisture content would be helpful in clarifying the effect of moisture distribution in foods, especially those with a moisture content so low that MRI cannot be applied. Finally, the development of a technique for the simultaneous visualization of the distributions of moisture and other constituents would greatly contribute to studies on changes in food properties during processing and optimization of unit operations, such as drying, in the food industry.

Moisture proﬁles which develop in the product during drying can have a high impact on the drying kinetics and the development of product quality parameters such as mechanical properties, porosity and shape. Drying of rice at high intensities results in ﬁssuring and subsequent breakage of the rice kernel which must then be rejected. The mechanical strength of a paper is established in the drying section; uneven drying of a paper web builds up stresses in the sheet which can result in surface wrinkles of cardboard material, poor printing properties and curl or twist of printing paper, and wavy copies from the laser printer. For clay products it is essential that the ﬁnal bricks all have the same size and shape after the drying and heat treatment processes. Knowledge of moisture proﬁles is also of importance for proposing drying mechanisms and determining rate limiting processes during drying as well as for validation of different modeling tools for the drying process. The techniques used to determine the moisture proﬁles can be classiﬁed as invasive or non-invasive. Invasive methods have the common feature that they disturb or interrupt the drying process. One example of an invasive method, which is also destructive, implies cutting the sample into a number of pieces and determining the moisture content in each sample (see Chapter 2). The method requires a sample large enough to be cut or sliced into at least ﬁve pieces and a drying process where the time for dividing the sample is signiﬁcantly less than the drying time. Suitable products for this method could be wood or larger fruits such as apples or pineapples. The moisture proﬁles as a function of time can be measured by repeating the process for different drying times. The method is based on a simple principle but has the disadvantages that the sample will be destroyed and for some products, such as fruits, it could be difﬁcult to ﬁnd samples that are identical in size and shape for a number of repetitive tests. It can also be questioned whether the cutting process has any inﬂuence on the measured moisture content. Another example of an invasive method is to build up the product from a number of slices from the same material, perform the drying process, separate the slices after

a given time and determine the moisture content in each slice. This method has been used by a large number of investigators for studying the drying of paper but this method could also be suitable for textile materials. The advantage is again the rather simple experimental set-up which is needed and the possibility of performing both conductive and convective drying experiments. It could be questioned whether sandwiching a number of slices will produce one homogenous material. Pores in the material will be interrupted at the interfaces between the slices which will result in different capillary forces and thus also different liquid transport in the layered composite. Another drawback is that the resolution of the method is limited to the thickness of the individual layers. Non-invasive methods offer the possibility to obtain a large number of moisture proﬁles during the drying operation without destroying the product. The most common non-invasive methods are magnetic resonance imaging (MRI), neutron scattering and X- or g-ray attenuation methods. Dielectric and infrared techniques have also been proposed for some applications. MRI has developed into a standard instrument for medical applications but has also been used to measure moisture proﬁles in a large number of products, such as apples, corn, rice, model food gels, wood, plywood, cardboard, paper, concrete, cement and catalyst pellets (compare with Section 1.4.5). More data are given by Harding et al. (2001); Bucur (2003); Hills (1998). To obtain moisture proﬁles in the sample the instrument is set up to measure the concentration of hydrogen atoms in liquid water. Normally the concentration of gaseous water is too low to be detected by the instrument, and hydrogen atoms in solid matter (cellulose, proteins etc.) have very short relaxation times which cannot be recorded with standard MRI techniques. The sample is subjected to a strong magnetic ﬁeld inside a superconducting magnet so that the size of this magnet also limits the size of the sample. The magnetic resonance frequency depends on the magnetic ﬁeld, and by creating gradients in the magnetic ﬁeld in different directions a resolution in space can be obtained. The noninvasive, non-destructive principle makes MRI an attractive tool for obtaining moisture proﬁles for a large range of products. The method can be designed to give 1D, 2D or 3D images of the water distribution in the product with a resolution in space down to 10 mm and a temporal resolution down to about 1 s. Data on the mobility, the diffusion coefﬁcients of water within porous products and on the pore size distribution can also be measured. To obtain a high resolution the sample size is limited to about 10 mm so that great care is needed when designing the experimental set-up. This also limits the energy supply for the drying process to convective transport from air at a temperature of about 100 C, resulting in rather low drying rates. Some other drawbacks using this technique are that the instruments are expensive and require skilled personnel for operation and setting the machine parameters in an optimal way. g-Ray attenuation methods have been discussed by Bucur (2003) and used by Stammer and Schl€ under (1993) during microwave drying of two ceramic materials. Neutrons interact preferentially with protons, thus they are absorbed selectively by water in moist products. Neutron beam attenuation was used by Ketelaars et al. (1992)

3.2 Principles of MRI for Determination of Moisture Profiles

for the determination of moisture gradients during the drying of clay samples. The disadvantage with the g-ray method is a spatial resolution limited to around 1–2 mm. The neutron beam method requires a neutron source, normally only available at a nuclear reactor. In this chapter the principles, the advantages and the limitations of the MRI method for obtaining moisture proﬁles and drying curves will be presented. Applications and results of the method will be presented for paper, pulp, wood and for different food products. The measurement of diffusivities will be brieﬂy presented and the use of the resulting data discussed.

3.2 Principles of MRI for Determination of Moisture Profiles 3.2.1 General Considerations

Non-invasive assessment of moisture migration in multicomponent products can yield valuable data for the development and validation of transport models. One of the most outstanding non-invasive techniques available for studying the status of water in materials is MRI, as mentioned earlier. Contrast in MRI images is governed by the local physicochemical properties of the system. The ability of MRI to provide spatially resolved information non-invasively, and without the use of ionizing radiation or contrast agent, is especially attractive for the study of multicomponent systems. The different time scales of moisture transport require protocols where different compromises are made with respect to the acquisition time and the resolution of mobility regimes. Within applications of MRI, there is always a trade-off between the following requirements: . . . .

sensitivity spatial resolution temporal resolution the range of molecular mobility regimes that can be studied.

When one of these requirements is favored, this will always be at the expense of at least one of the other three. Hence, to yield valuable information, the development of an experimental MRI protocol involves a careful balance of these four requirements. The aim of this section is to introduce the basic concepts necessary for the understanding of MRI signal dependence upon intrinsic parameters of the sample (relaxation times, self-diffusivity etc.), and extrinsic parameters (magnetic ﬁeld strength, sequence parameters, temperature etc.). Here we deal with only one species: water protons (1 H). In order to heighten the awareness of the advantages but also the constraints of the MRI approaches, the limits of the technique are discussed. For more details on the theoretical principles of MRI, the reader is referred to the books by Hills (1998); Callaghan (1991).

3.2.2 Basic NMR 3.2.2.1 Nuclear Magnetic Moment and Larmor Relation Nuclear magnetic resonance is based on the absorption and emission of energy in the radiofrequency (rf ) range of the electromagnetic spectrum. Many nuclear particles possess the property of spin, that is an intrinsic angular momentum. Magnetism is a phenomenon caused by electric charge in motion (like protons). NMR relies upon the ! fact that the elementary magnetic moment m thus created, which is collinear to the angular momentum and associated to the nucleus of the atom (such as the hydrogen proton 1 H), precesses at an angular frequency v0 when submitted to an external ! magnetic ﬁeld B0 , see Fig. 3.1. The angular frequency is directly proportional to the magnetic ﬁeld strength

v0 ¼ gB0

ð3:1Þ

In Eq. 3.1 g is the gyromagnetic ratio, a characteristic of the observed nucleus (for hydrogen, g ¼ 42.58 MHz T1). This relation is known as the fundamental Larmor relation.

Fig. 3.1 Precession of the magnetic moment in the static B0 magnetic field.

3.2.2.2 Net Magnetization and Radio Frequency Excitation The sum of the individual magnetic moments (or spins) of identical particles (such as water hydrogen) contained in a macroscopic sample gives a net magnetization ! M. At equilibrium, this net magnetization vector M lies along the direction of ! ! the applied magnetic ﬁeld B0 and is called the equilibrium magnetization M0 (Fig. 3.2a). Adopting the conventional NMR coordinate system, the external ! ! magnetic ﬁeld B0 and the net magnetization vector M 0 at equilibrium are both along the z axis. As in all spectroscopic techniques, signal receipt needs a prior perturbation of the system. For NMR, this perturbation is created by electromagnetic radiation, which consists of a radiofrequency excitation pulse at the appropriate frequency n0 ¼ v0/2p. ! This radiation is generated by an rf-coil placed around the sample, which creates a B1 ! ﬁeld perpendicular to B0 . The perturbation induces a resonant phenomenon that

3.2 Principles of MRI for Determination of Moisture Profiles

Fig. 3.2 The three basic states of an NMR experiment (a) M0 at equilibrium, (b) excitation by a radiofrequency pulse, (c) relaxation.

!

leads to a rotation of M0 at an angle u (Fig. 3.2b). The value of u depends on the rf-pulse duration tp: ð3:2Þ

u ¼ gB1 tp !

!

After the rf-excitation is turned off, M 0 precesses at a frequency n0 around B0 (Fig. 3.2c), and returns gradually to its thermodynamic equilibrium position along the z axis in the course of a relaxation process. To facilitate the vectorial description of this relaxation phenomenon, it is useful to deﬁne a frame of reference that rotates ! around the z axis at the Larmor frequency. Thus, the magnetization vector M 0 rotating at n0 in the laboratory frame appears stationary in the frame of reference and ! ! can be decomposed into two components: one longitudinal, ML , aligned with B0 , and ! ! another transversal, M T , in a plane perpendicular to B0 , see Fig. 3.3. 3.2.2.3 Relaxation and NMR Signal ! Figure 3.4 illustrates the return of M0 to equilibrium after an rf-pulse of 90 . The ! ! evolution of the two components ML and M T with time (in the rotating frame) is described by the following expressions:

ML ðtÞ ¼ M0 ð1exp ðt=T 1 ÞÞ

ð3:3Þ

MT ðtÞ ¼ M0 exp ðt=T 2 Þ

ð3:4Þ

We note that the two processes are exponential and separated. They are character! ized by the time constants T1 and T2. T1 related to the longitudinal component ML is called the longitudinal (or spin–lattice) relaxation time. It is due to energy exchange

Fig. 3.4 Amplitude of the longitudinal and transversal components during T1 and T2 relaxation, given by Eqs. 3.3 and 3.4.

between the spins and surrounding lattice, re-establishing thermal equilibrium. T2, ! related to the transverse component MT is called the transverse (or spin–spin) relaxation time. It results from spins getting out of phase in the plane perpendicular ! to B 0 due to local interactions between spins. ! The electric signal induced by the decay of the transverse component M T during the relaxation is then detected with a receiver rf-coil (it is often the same as that used to generate the rf-pulse excitation) and constitutes the observed NMR signal (called a free induction decay (FID)). This time-dependent signal is then Fourier transformed (FT) to obtain the associated frequency signal (or frequency spectrum). Because all water protons contained in a homogeneous or heterogeneous sample have, theoretically, the same angular frequency, the frequency spectrum has only one peak, see Fig. 3.5. The natural line width at half maximum intensity n1/2 is related to T2 by: y 1=2 ¼

1 pT 2

ð3:5Þ

Often lines are broader. For example, in solids or for slowly tumbling molecules in liquids, magnetic dipole–dipole interactions between nuclei lead to appreciable line broadening, sometimes by several kHz. In a perfectly homogeneous ﬁeld B0, the time constant of the decay would be T2. However, this it is not the case in practice, because nuclei in different parts of the sample experience slightly different values of the ﬁeld B0. Hence, resonance takes places at slightly different frequencies. Thus, the free induction signal decays in a time T 2 < T 2 deﬁned by: 1 1 þ gDB0 ¼ pT 2 pT 2

Fig. 3.5 Envelope of the free induction decay and its Fourier transform.

ð3:6Þ

3.2 Principles of MRI for Determination of Moisture Profiles

Fig. 3.6 Different relaxation regimes as function of tc (v0 is given by the magnetic field strength, cf. Fig. 3.1).

This time includes contributions from both natural line width and magnetic ﬁeld inhomogeneity DB0. 3.2.2.4 Factors Influencing Relaxation Times Relaxation characteristics depend on the physicochemical properties of the system studied and more speciﬁcally on the molecular correlation time, t c, that can be deﬁned as the average time between molecular collisions for a molecule in some state of motion. One should note that t c is related to the viscosity and the temperature of the system by the proportionality relation t c / m/T. Figure 3.6 represents schematically the dependence of relaxation times on molecular correlation time and angular frequency via the product v0tc. Three main regimes can be distinguished: .

.

.

For v0tc 1, corresponding to non-viscous liquids (region A in Fig. 3.6), it is T1 T2 (typically 3 s for pure water at 25 C), and both relaxation times decrease with increase in tc or v0. In viscous liquids or non-rigid solids (v0t c > 1) T2 decreases and T1 increases with v0t c, and it is T1 > T2 (region B in Fig. 3.6). Such conditions typically prevail in the case of biological tissues, with T1 and T2 values about 1 s and a few tens of ms, respectively. The third region (region C at v0t c 1) concerns rigid lattices for which T2 is very short (<10 ms) and T1 T2 (T1 10 s).

Knowledge of the intrinsic parameters T1 and T2 is essential for the quantitative determination of water distribution in a heterogeneous sample. 3.2.3 Imaging Principles

As we have seen previously, the NMR frequency signal associated with the water protons contained in a sample appears as only one line. This line does not provide any information about the spatial variability of water distribution inside the sample. It is, therefore, necessary to encode the signal in space. To illustrate this space encoding, a

Fig. 3.7 Principle of measurement of sample projection with the help of a magnetic gradient in the r-direction, Gr.

phantom constituted of two rectangular boxes ﬁlled with water at two different levels is used, see Fig. 3.7. 3.2.3.1 Projection of an Object (1D Imaging) ! The basic idea of MRI is to superimpose to the magnetic ﬁeld B 0 a magnetic gradient Gr, which varies linearly in the space direction r. The angular frequency then becomes dependent on the position r :

vðrÞ ¼ v0 þ gGr r

ð3:7Þ

This ﬁrst encoding step ( frequency encoding) allows one to obtain a relation between proton frequency and water localization. As illustrated in Fig. 3.7, after one-dimensional Fourier transformation (1D-FT) of the NMR signal created in this way, the projection of the object along the r direction is obtained. 3.2.3.2 Two-Dimensional Imaging ! ! After the rf-excitation of M0 , the created M T transverse magnetization, then submit! ted only to the ﬁeld B 0 , is dephased by an angle F expressed by the integral: ðt ð3:8Þ FðtÞ ¼ v0 dt 0

If a ﬁeld gradient Gp is superimposed to B 0 along a direction p, the combination of ! Eqs. 3.7 and 3.8 leads to a phase dependence of MT on the position p: ðt

ðt

Fðt; pÞ ¼ vðpÞdt ¼ ðv0 þ gGp pÞdt 0

ð3:9Þ

0

This permits a second spatial encoding step (phase encoding). The combination of frequency and phase encoding allows, after double Fourier transformation (2D-FT), a two-dimensional image to be obtained in the plane (r, p), see Fig. 3.8. 3.2.3.3 Slice Selection As mentioned above in Eq. 3.7, a ﬁeld gradient G induces an angular frequency dispersion of water protons, in relation to their position along the applied gradient direction. If an excitation rf-pulse of restricted frequency range (called a selective pulse) is applied simultaneously to this gradient, only one slice in the sample will be excited, see Fig. 3.9.

Fig. 3.9 Principle of slice selection by use of a selective pulse of bandwidth Dvs and simultaneous application of a gradient Gs. This method selects spins which precess at the frequencies corresponding to the bandwidth of the selective pulse. These spins belong to a slice perpendicular to the s-gradient direction.

The slice thickness (Sthick) can be controlled by the choice of gradient strength (Gs) and/or frequency range selectivity (Dvs) of the rf-pulse: Sthick ¼ Dvs =gGs

ð3:10Þ

The applied Gs deﬁnes also the selected slice orientation, perpendicular to the gradient direction. Note that linear combinations of x, y, and z magnetic ﬁeld gradients allow oblique imaging to be performed. In this way, any image orientation in the object can be produced. 3.2.3.4 Three-Dimensional Imaging There are two main approaches to obtaining a 3D image of an object.

3.2 Principles of MRI for Determination of Moisture Profiles

The ﬁrst consists in repeating the slice selection process described previously over the sample. It can be thought of as collecting several contiguous slices through the imaged object. The second is based on two separate phase encodings and one frequency encoding. No slice selection is required. This latter encoding mode will not be detailed here; more information can be found in Brunner and Ernst (1979). 3.2.4 Imaging Sequences

An imaging sequence consists of interlaced rf-pulses and gradients. There is a great number of possible sequences, depending on what we want to see, but also on what we can see. Here, only the two basic spin-echo and gradient echo sequences will be introduced, to reveal the importance of the extrinsic and intrinsic parameters on the nature of the signal obtained, in particular on the quantitative aspects. Some others sequences such as parametric imaging and solid-like imaging could be of interest for particular applications in the context of this chapter, but will not be discussed in detail. 3.2.4.1 The Spin–Echo (SE) Sequence The spin–echo sequence is the basic MRI sequence described by Fig. 3.10. The amplitude of the signal in each voxel (v) of the image is given by the expression:

Av ðSEÞ ¼ krv ð1expðT R =T 1;v ÞÞexpðT E =T 2;v Þ

ð3:11Þ

where k is a constant which depends on the imager characteristics, TR and TE are the repetition and echo times which are the characteristic delays of the sequence, rv is the volumetric proton density, and T1,v and T2,v are the longitudinal and transverse relaxation times of water protons contained in each voxel.

3.2.4.2 The Gradient–Echo (GE) Sequence In a gradient echo sequence, a gradient is used instead of a 180 rf pulse to rephase the spins, see Fig. 3.11. The amplitude of the signal in each voxel of the image can now be expressed as

Av ðGEÞ ¼ krv ð1expðT R =T 1;v ÞÞexpðT E =T 2;v Þ

sin a 1expðT R =T 1;v Þcos a ð3:12Þ

For a ﬁxed TR/T1 ratio, the optimal a angle (Ernst angle), for which the signal amplitude is maximal, is extracted from the relation: cos a ¼ expðT R =T 1 Þ

ð3:13Þ

Imaging with a gradient echo is intrinsically more sensitive to magnetic ﬁeld inhomogeneities, and also to magnetic susceptibility differences that can exist in the sample (for example at air/water interfaces), because of the use of the refocusing gradient. On the other hand, use of a small ﬂip angle a and of a gradient for refocusing the magnetization vectors provide this sequence with a time advantage. Therefore it is widely used for fast scan images, including 3D acquisitions.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples 3.3.1 Some General Data about the Materials

Paper is built up of a porous network of cellulose ﬁbers with typical diameters of 15–30 mm and lengths of 1–5 mm as well as some ﬁllers and chemical additives. The

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

ﬁbers are oriented in the plane of the paper with a preferred orientation in the machine direction (explained in the following). The paper is made on a paper machine as a continuous web 5–10 m wide by forming the paper structure from a suspension of 0.5–1% of cellulose ﬁbers. The water is subsequently removed in the forming, in the press and in the drying sections so that the ﬁnal paper contains 93–97% of dry matter. The basis weight of a paper is given by the total amount of dry matter content per square meter of paper. It varies from 40 g m2 for newsprint up to about 500 g m2 for high basis weight cardboard. This parameter is often used to deﬁne the experimental conditions and gives a clear indication of the thickness of the paper studied. Two different porosity scales exist in paper. The inter-ﬁber pores are pores that are formed between the ﬁbers with pore sizes of the order of 0.5–10 mm. The intra-ﬁber pores are pores in the walls of the cellulose ﬁbers with sizes below about 1 mm. Initially both inter- and intra-ﬁber pores are saturated with water. As the web dries, ﬁrst the inter-ﬁber water is removed, followed by removal of the water in the intraﬁber pores. The intra-ﬁber pores collapse during dewatering, so that essentially non-porous ﬁber walls are obtained. One parameter of importance for the discussion of water removal is the ﬁber saturation point (FSP), which is the total amount of water that can be contained in the intra-ﬁber pores. Typical values are in the range of 1–2 g water/g solid – depending on the type of trees used, the pulping process (chemical, mechanical etc.) and the treatment in different processing steps. In this context it should be noted that cellulose is a hygroscopic material with a maximum hygroscopic moisture content of about 30%. The properties of the web and the ﬁnal paper (such as basis weight, mechanical strength etc.) vary with the following directions: .

.

.

MD, machine direction; the direction in which the web moves in the paper machine; CD, cross-direction, across the width of the web and perpendicular to the machine direction; ZD, z-direction, the thickness direction perpendicular to the plane formed by MD and CD.

A pulp sheet is essentially a paper with a random or oriented distribution of ﬁbers in the plane and a basis weight of 750–1500 g m2, resulting in a thickness of about 1.5–3 mm. Moisture transport in cellulose structures is of high importance in a number of processing steps, in the retailing step as well as during ﬁnal consumer applications. During drying of paper most of the water is initially located in the intra-ﬁber pores. Water will either evaporate in these pores and diffuse in the gas phase to the surface of the paper or migrate as a liquid to the surface and evaporate there. Since the dry ﬁber is non-porous, the result is shrinkage in the CD and ZD of the web. This has a strong inﬂuence on a number of quality parameters such as tensile strength, sheet ﬂatness and surface smoothness. Another application that involves moisture transport is the coating process, where a coating color layer is applied to a dry base paper resulting in

transport of water and chemicals into the base paper. Typical ﬁnal consumer applications of moisture transport are water uptake in baby diapers and soaking of water in corrugated packages resulting in loss of mechanical strength. 3.3.2 Overview of Previous Results 3.3.2.1 Pulp, Paper and Cellulose Samples The ﬁrst application of the MRI technique to study water distribution and transport in paper or pulp samples was reported by Nilsson et al. (1996). In their work the water distribution in a 4 mm thick cellulose cylinder was measured with a Bruker 24/30 MR imager with a magnetic ﬁeld strength of 2.4 T. The sample consisted of a 42 mm cylindrical plug of pulp which was prepared from dry commercial sulfate softwood pulp. The sample was dried by blowing room-temperature air over the sample holder, resulting in drying times of over 3 h, approximately 50 times longer than under industrial conditions. The instrument was used with a TR time of 2 ms and a TE time of 1.1 ms, and a spatial resolution of 0.39 mm was obtained. By using pulp slices with different known moisture contents a linear correlation between the moisture content of the pulp samples and the MRI signal was established. The experimental conditions resulted in an average drying rate of 8 105 kg m2 s1. It could be shown that the drying took place at a decreasing drying rate. Bell-shaped curves were obtained for the moisture distribution. The experiments were later improved by Bernada et al. (1998a,b), to reach a higher spatial resolution and a higher drying rate, that means conditions more representative of those employed in the industrial process. This was accomplished by increasing the drying air temperature and using industrial pulp sheets. The authors were able to measure the distribution of water with a spatial resolution of 0.15 mm during the drying of samples approximately 2.5 mm thick. The improvements in spatial resolution were brought about by improvement in imaging hardware, the use of a higher ﬁeld magnet and modiﬁcations of the imaging protocol. Evaporation could take place from both surfaces of the samples. Drying times were about 10 min for the highest temperature used (87.5 C), or about twice the time applied in an industrial dryer. The moisture proﬁles measured at this temperature are shown in Fig. 3.12. The curves are bell-shaped and somewhat shifted to one of the open surfaces, indicating that transport to this surface is enhanced by higher heat or mass transfer coefﬁcients. Leisen et al. (2001) studied in-plane moisture transport for a number of cellulose samples. The samples were handsheets, paperboard and a polyethylene-coated paperboard with thicknesses between 0.53 and 2.1 mm. The ratio of the sonic moduli MD/CD ranged between 1.7 and 6.8, showing a strong variation of the anisotropic ﬁber orientation of the samples. The samples were studied in a Bruker instrument with a magnetic ﬁeld strength of 9.4 T. The drying time was about 8 h, and the images showed annular patterns of reduced intensity as the samples dried from the outside edge. No anisotropy could be detected for the moisture proﬁles and, thus, the diffusional resistance should have been the same in all directions of the plane.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

Fig. 3.12 Moisture profiles obtained by Bernada et al. (1998b) at an air temperature of 87.5 C and a relative humidity of 4 %. Drying times between 0 and 14 min.

In a subsequent work Leisen et al. (2002) studied diffusion in paper at moisture contents below 20%, thus in the hygroscopic range for the product. This is a more challenging task due to the lower amounts of water and the increased interactions with the solid phase. The paper samples used were prepared from southern pine bleached kraft and consisted of two sheets each with a basis weight of 468 g m2. The average sheet thickness of the dry sample was 1.2 mm. Samples with a diameter of 17 mm were analyzed in the instrument. Their moisture uptake was studied by placing them between a humid environment obtained from distilled water and a dry environment established by locating a dessicant on top of the paper sample. Because of the low moisture contents in the paper, the acquisition times were up to 68 min. The results show that quite long times are needed to establish equilibrium between the gas and the solid phases. When moisture could penetrate through only one surface, equilibrium was not established at the ﬁnal experimental time of about 55 h, while when moisture could penetrate through both surfaces some kind of equilibration could be seen after 3 h. Finally a model was developed, which was able to describe the gas diffusion in the inter-ﬁber pores and liquid diffusion in the solid cellulose. Harding et al. (2001) presented moisture proﬁles during drying of industrial cardboard samples at a resolution of 15 mm. These results will be discussed in more detail in Section 3.3.3.

3.3.2.2 Wood A very good overview of NMR and MRI for wood applications is given by Bucur (2003). This includes not only measurements of moisture proﬁles and self-diffusivities during drying but also describes how the techniques have been used to study wood structure and decomposition processes taking place in this material. A relatively large number of publications deal with the interactions between water and wood and the determination of moisture content while the number of publications on applications of the technique to drying is rather limited. Some results have been presented by Lindgren (1994) with one-dimensional images of pine during drying from a moisture content of 27 to 11%. Other results for wood were communicated by Flibotte et al. (1990) and Olson et al. (1990). Menon et al. (1987) were one of the ﬁrst groups to use NMR for the quantitative measurement of water in wood materials. In this work fundamental data for the free induction decay were presented and these data, together with knowledge about the composition of the wood, were shown to give the same values for the total moisture content in the wood sample as is traditionally achieved from the oven-dry method. Drying was used as a means to change the average moisture content but no moisture proﬁles were measured in the samples. Rosenkilde (2002) investigated a number of different techniques (slicing, X-ray tomography, MRI) for measuring the distribution of moisture in wood samples during drying. Using X-ray the resolution was limited to 240 mm and, since this technique measures the overall density of the material, the solid density must be known in order to calculate the moisture content at different positions in the sample. This led the author to prefer the MRI technique for analyzing moisture gradients at small distances from the surface of a wood cylinder during drying (Rosenkilde and Glover, 2002; Rosenkilde et al., 2004). In the ﬁrst set of experiments, samples of Scots pine shaped as cylinders with a diameter of 14 mm and a length of 20 mm were used (Rosenkilde and Glover, 2002). The samples were sealed by means of plastic tape except on one end of the cylinder so that moisture transport took place through this surface. The initial moisture content was 1.16, and the samples were dried by blowing air with a velocity of 3 m s1, a temperature of 43–46 C and a relative humidity of 16–18% parallel to the open surface. The magnetic ﬁeld strength at the sample surface was 0.7 T and the ﬁeld strength normal to the wood surface was 17 Tm1 resulting in a very high resolution of 13 mm per pixel. The signal was converted to moisture content by comparing with the initial proﬁle in the sample which was assumed to be ﬂat. Some results for the moisture proﬁles are shown in Fig. 3.13. During the ﬁrst 4 h the proﬁles show a steep gradient in the ﬁrst 90 mm of the sample and are then almost ﬂat. Surface roughness was probably not the reason for the steep gradients at the surface. Other possibilities could be structural changes in the samples resulting in differences in the transport resistance for water or kinetics for the hygroscopic equilibrium between wood and the surrounding air. Hameury and Sterley (2006) used MRI to study the buffering capacity of wood materials to passively reduce the indoor humidity ﬂuctuations resulting from internal moisture loads and outside humidity ﬂuctuations. The moisture gradients were

measured in a 12 mm cylinder fabricated from Scots pine. One surface of the cylinder was exposed to step changes in the relative humidity between 20 and 80% and the moisture was recorded in the sample with a resolution of 127 mm and a total ﬁeld of view of about 27 mm. Since the average moisture content of the sample was only 7–9%, the water bound to the solid matrix had very short transverse relaxation times. This problem was overcome by applying a method based on the single-point imaging sequence, also known as constant time imaging. This sequence is similar to the SPRITE sequence presented by MacMillan et al. (2002). Good data were presented showing that the moisture exchange between the wood and the environment is limited to a few mm below the surface of the material. The moisture buffering value could also be predicted with good accuracy from the moisture proﬁles. van Houts et al. (2004, 2006) investigated by means of MRI the water penetration into two different sizes of oriented strandboard (similar to plywood). In the ﬁrst paper a micro-imaging instrument was used allowing samples with dimensions of 11 15 mm2 to be studied. The second study was conducted in a body scan instrument where 152 152 mm2 samples could be investigated. In a specially designed glass tube the samples were initially soaked with water, the water was removed and the concentration of water in the samples was measured. This procedure was repeated for the required number of times up to a total soaking time of 180 min. Water penetration could be monitored quite well but for some reason only the water in the voids of strandboard was detected but not the free water within the solid wood. The self-diffusivities for water in Douglas ﬁr were reported by MacGregor et al. (1983) to be 1.2 109 m2 s1 in the longitudinal direction of the ﬁbers and 0.36 109 m2 s1 in the direction perpendicular to the ﬁbers. This indicates that water mobility along the ﬁbers is higher than that in the transverse direction. The reported data are close to the data reported for cellulose ﬁbers in paper samples, see Section 3.3.3.5.

In this section the experiments performed by Harding et al. (2001) and Wessman et al. (2000) using MRI for determination of moisture proﬁles during drying of cardboard samples will be presented and discussed in detail. 3.3.3.1 Experimental Conditions A fresh, never previously dried composite cardboard sample taken after the press section from the production facilities of ASSI Dom€an Fr€ ovi was used in this study. It was stored in a cold room until the measurements were made. The storage time for the last piece of the sample was roughly 4 weeks. The cardboard is a three-layer composite with the composition described in Tab. 3.1. The CTMP (chemical thermo mechanical pulp) had undergone mild chemical and heat treatment as well as mechanical reﬁning which breaks up the lamellae in the ﬁber wall. The kraft pulp undergoes aggressive chemical and heat treatment during production which dissolves the lignin hence allowing the lamellae to separate and swell. Pulped broke refers to pulp from a bad batch that has been recycled – this could therefore contain pulp of any grade, with possibly smaller pores due to the initial drying process. The basis weight, dry thickness, density and initial water content of the complete composite sample and the three separated layers were determined by sample weighing and thickness measurements which were carried out in accordance with standard techniques (ISO 534). For the calibration, 3D imaging and diffusion experiments samples were slowly pre-dried to water contents of 1.0, 0.8, 0.6, 0.4, and 0.2. An additional sample was prepared by adding water to the cardboard sample to produce a water content of 2.0. The basis weight, dry thickness, density and initial water content of the complete composite sample and the three separated layers are given in Tab. 3.2. The error limits represent the standard deviation from measurements on four samples. The thickness of the composite sample is signiﬁcantly less than the sum of the thicknesses of the three individual layers once separated. This is due to the disruption of the ﬁber structure during the process of separating the layers. For this reason the thicknesses of the three layers after separation can only be taken as an indication of their relative thickness in the composite rather than as a measure of the absolute thickness of each layer in the sample. This result highlights the great advantage of non-invasive techniques such as NMR imaging that can monitor properties of the different layers without disrupting the ﬁber system. Tab. 3.1 Composition of the composite cardboard sample.

All NMR imaging and diffusion measurements were carried out using a Bruker DRX 400 spectrometer, equipped with micro-imaging accessories and an 8 mm coil, unless otherwise stated. The data were then transferred to the program Matlab for further processing and analysis. 3.3.3.2 Drying Experiments and MRI Parameters One of the particular challenges encountered when using MRI to study water distribution in wood pulp cellulose ﬁbers is the short T2 (spin–spin) relaxation time of the water. The T2 relaxation time is typically between 1 and 6 ms and decreases with decreasing water content. Special attention was therefore paid to the choice of imaging procedure. A one-dimensional spin–echo method was chosen to allow fast acquisition times, maximize signal to noise and prevent susceptibility problems associated with gradient reversal methods. However, if the echo time employed in the imaging sequence is not less than about ﬁve times the T2 relaxation time, the signal recorded will be attenuated – and thus not directly a true representation of the water content in the sample. For this reason efforts were made to minimize the echo time. The effects of T2 attenuation were directly accounted for also by explicitly measuring the T2 relaxation time of the water across the proﬁles at each time point. The geometry of the cell and sample positioning was chosen to ensure onedimensional mass transport in the region of interest during drying and the imaging experiment was designed to yield one-dimensional water concentration proﬁles across the thickness of the cardboard sample. A specially designed Teﬂon sample holder was built to hold the cardboard sample in a vertical position within an open ended 8 mm glass tube, as shown schematically in Fig. 3.14. A section of the wet cardboard, approximately 30 mm by 7 mm, was cut and placed in the holder, positioned in the coil of the NMR probe. A small funnel was ﬁtted to the base of the tube to form a seal with the air supply outlet. The air temperature was controlled using a thermocouple and a heating element within the NMR imaging probe head. The sample was positioned across the diameter of the tube so that the drying air stream ﬂows evenly over the two faces of the cardboard allowing the sample to dry from both surfaces. The sample was positioned in a random orientation in the x–y plane (deﬁned in Fig. 3.14) so that any non-uniformity in the air ﬂow through the probe would not lead to systematic artifacts in the ﬂow pattern over the cardboard sample.

Prior to the start of drying an initial horizontal 2D cross-sectional image of the cardboard sample was acquired to determine the orientation of the sample within the x–y plane. The direction of the 1D proﬁle was then set so that it was aligned perpendicular to the surface of the cardboard – across the thickness of the sample. The slice selection gradient was aligned parallel to the surface of the cardboard so as to selectively image only the central region of the cardboard sample. This eliminated the signal from the cardboard near the sample holder which may prevent evaporation from this region. The sample positioning procedure took approximately 4 min. After the air ﬂow was started the series of experiments were performed at regular intervals until the signal intensity had dropped below the noise level or no further signal intensity loss occurred. A spin–echo {90 (hard) – 180 (soft) – echo} pulse sequence was used for 1D proﬁling. Proﬁles containing 128 points were acquired across a ﬁeld of view of 2 mm giving a spatial resolution of 15.6 mm/pixel. The slice thickness of the proﬁle was 2 mm and slice selection was achieved by application of a 250 ms Gaussian soft pulse in combination with a 3 G cm1 gradient. A spectral width of 100 kHz was used for data acquisition and the read gradient strength was 178 G cm1, giving an echo time of 1.625 ms. A repetition time of 6 s was used and typically four scans were co-added giving a total acquisition time of 24 s. A long repetition time was used to minimize effects due to T1 attenuation. In addition, after the acquisition of each proﬁle a series of eight T2 weighted proﬁles were obtained by using a pre-conditioning Hahn echo module {90 (hard) – tT2/2 – 180 (hard) – tT2/2 – proﬁle} prior to the proﬁle acquisition with additional T2 delays, tT2 of 0.2, 0.4, 0.8, 1.2, 1.6, 2, 4 and 6 ms. The intensity of each point in the proﬁle, S, in the set of T2 weighted proﬁles acquired

where S(0) is the signal intensity corrected for the effect of the delay tT2. The proﬁle of T2 relaxation times was then used to correct the signal intensity in the proﬁle for attenuation due to the echo time of 1.68 ms implemented in the proﬁling sequence. Before the start of drying and at regular intervals during drying at the slower drying rates studied, a set of T1 weighted proﬁles was also acquired using a pre-conditioning inversion recovery module {180 (hard) – tT1 – proﬁle} prior to proﬁle acquisition. The intensity of each pixel, S, in the set of T1 weighted proﬁles acquired with delay tT1, was ﬁtted to S tT1 ð3:15Þ ¼ 12exp T1 Sð0Þ where S(0) is the signal intensity corrected for the effect of the T1 weighting delay tT1. During drying at the slower drying rates studied two-dimensional slice selective images were also acquired with the help of a spin–echo slice selective imaging sequence. The read direction was oriented across the thickness of the cardboard. The ﬁeld of view was 2 and 8 mm in the read and phase directions, respectively. The image size was 128 16 providing a spatial resolution of 15.6 and 500 mm/pixel, respectively. The slice thickness was 8 mm. Typically, a repetition time of 4 s was used and 2 scans were co-added giving a total acquisition time of just over 2 min. Five different drying conditions were studied and the air temperatures, air ﬂow rates and air humidities used are given in Tab. 3.3. The air humidity was controlled by bubbling through a cylinder of water before passing the air into the imaging probe. Air moisture content was calculated from the wet and dry bulb temperatures. Three to six individual drying experiments were performed for each of the ﬁve drying conditions described in Tab. 3.3. By repeating the experiments, the reproducibility of results and the effects of sample variability could be assessed. 3.3.3.3 Calibration Procedure In order to test the quantitative nature of the proﬁling, experiments were carried out on samples prepared with water contents of 2.0, 1.0, 0.8, 0.6, 0.4, and 0.2 as well as on the original wetted sample (with a water content of 1.45). These samples were placed Tab. 3.3 Air temperatures, air flow rates and air humidities used in cardboard drying experiments.

in the cardboard holder and sealed using polymer ﬁlm to prevent drying during the measurement procedure. One dimensional proﬁles, T1 and T2 relaxation weighted proﬁles and slice selective images were acquired as described above for the drying experiments. A capillary containing water with a small amount of copper sulfate to reduce the T1 relaxation time to approximately 1 s was then placed adjacent to the cardboard sample. The imaging experiments were repeated using a ﬁeld of view of 4 mm (rather than 2 mm) across the sample thickness to allow the capillary to be simultaneously imaged. The use of the capillary as a reference sample allowed the water signal intensity from the cardboard to be directly quantiﬁed. By comparison of the directly quantiﬁed proﬁles with the proﬁles acquired without the reference capillary, using the same imaging scheme as applied in the drying experiments, a scaling factor was determined. This factor was then used to convert the signal intensity of the proﬁles acquired during drying into a water concentration. On some of the calibration samples relaxation weighted proﬁles were acquired using up to 32 variable delay times to test the assumption that the signal is characterized by a single relaxation time constant at each spatially resolved point. Water concentration proﬁles, and proﬁles of the water T1 and T2 relaxation constants for the calibration samples studied are shown in Fig. 3.15. In this and

in all other comparable ﬁgures the cardboard proﬁles shown have been oriented such that the top layer described in Tables 3.1 and 3.2 is to the left-hand side of the proﬁle. For all the calibration samples studied the T1 and T2 weighted proﬁles showed a good ﬁt to Eqs. 3.14 and 3.15, which assume a single relaxation constant at each spatially resolved point. This was true even when up to 32 variable time delays were acquired and used in the ﬁtting procedure. The T2 relaxation time of the water in the cardboard decreased signiﬁcantly with water content, varying from around 4.8 ms for a sample a with water content of 2.0 to 2.1 ms for the sample with a water content of 0.2. The T2 relaxation time was fairly constant across the sample, but showed a slightly higher value in the lower layer. The T1 relaxation time showed a similar decrease with water content. However, for all calibration samples studied, the T1 relaxation time in the upper layer was signiﬁcantly longer than in either the middle or lower layers. This could be a consequence of the bleaching process – perhaps removing some impurities that act to reduce the T1 relaxation time of water in the other, nonbleached layers. The water concentration proﬁles shown in Fig. 3.15a have been extracted from two-dimensional cross-sectional images by averaging over the central 4 mm region of the cardboard sample in the image. The proﬁles were scaled to the intensity of the water from the capillary placed adjacent to the sample and corrected for the effects of relaxation contrast according to Eqs. 3.14 and 3.15. By scaling to the intensity of pure water the proﬁles could be made quantitative and expressed in terms of g cm3. The total amount of water in the calibration samples was calculated by summing across the water concentration proﬁles and dividing by the pixel resolution (15.6 mm). Figure 3.16 shows the calculated total water mass per area (in g m2) as a function of the water content of the calibration samples. Error bars represent standard deviation between proﬁles extracted at varying positions across the two-dimensional image of each sample. Linear ﬁt to the data gave a slope of 168 3 g m2 before correction for

Fig. 3.16 Total water determined from NMR profiles versus water content of samples before (&) and after (*) correction for relaxation effects.

relaxation effects and 225 6 g m2 after correction. The data show that the total amount of water in the samples determined by the NMR imaging experiments is directly proportional to the water content determined by sample weighing. The gradient of the linear ﬁt is slightly lower than the measured basis weight of the cardboard (239 2 g m2), but this difference may be due to water loss during sample transportation, positioning in the magnet and general sample variability. Also shown in Fig. 3.16 is the total water that would be determined from the results if no correction were made for relaxation contrast effects. A linear ﬁt to this uncorrected data has a signiﬁcant non-zero intercept and a lower slope than the relaxation corrected data. This emphasizes the need to correct for relaxation contrast in order to obtain quantitative proﬁles during the whole of the drying process. The water concentration proﬁles of the calibration samples and the initial proﬁles acquired in the drying experiments clearly show a higher water concentration in the two outer layers than in the middle layer. Assuming that the thicknesses of the three layers are in the same proportion to each other in wet and dry samples, the relative concentration of water in the three layers can be calculated from the data shown in Tab. 3.2 to be 0.42 0.06, 0.24 0.02 and 0.33 0.02, respectively. This can be compared with the ratios determined by averaging all initial proﬁles acquired in the drying experiments. The water concentration in each layer was determined by dividing the total proﬁle into regions in the proportion of the dry layer thickness and then averaging across the central half of each layer. This gave relative water concentrations in the three layers of 0.38 0.02, 0.26 0.01 and 0.35 0.3, respectively. The errors quoted represent the standard deviation between samples and within these errors the ratios determined from the NMR imaging proﬁles are in agreement with those determined by standard weighing and measuring techniques. 3.3.3.4 Results for Drying Profiles Figure 3.17 shows typical results for the temporal evolution of the water concentration proﬁles across the thickness of cardboard samples drying under varying conditions. The proﬁles were corrected for T2 relaxation attenuation and then scaled to units of g cm3 using the scaling factor determined from the calibration experiments. Due to the variation in the time scale over which drying occurs the time interval between successive proﬁles is different for the different drying conditions. Clearly the outer layers of the cardboard initially contain more water than the middle layer. It should be pointed out again that the samples have been taken after the press section of an industrial machine and have been stored in a cold room for 1–4 weeks. The outer layers consist of bleached kraft pulp, most probably with a higher FSP than the middle layer where the main component is a mechanical pulp. The moisture distribution in the layers as the paper leaves the press section could not be measured and thus it is difﬁcult to argue if the proﬁles measured are the actual proﬁles on the machine or a result of moisture redistribution phenomena until the measurement took place. However, considering the FSP-values discussed above it seems reasonable that the proﬁles measured are also the proﬁles on the machine.

Initially more water is removed from the outer layers, resulting in a paper with relatively even moisture content. The bell-shaped proﬁles reported by Nilsson et al. (1996) and Bernada et al. (1998a,b) could be observed in run A but were not clearly seen in the other experiments. Instead moisture gradients appeared at the surfaces (considering shrinkage) while the moisture content inside the sample was close to constant. This indicates a rather rapid redistribution of water in the middle layer caused by high liquid diffusivities. These results were not conﬁrmed by the diffusion measurements, see Section 3.3.3.5. During drying the water concentration proﬁles decrease in intensity and width with time. Figure 3.18 shows that the width of the water proﬁle with an intensity above 0.1 of the maximum decreases approximately linearly with the water content, approaching the dry cardboard thickness in the limit of low water content. Moreover, the data follow the same trend as for the calibration samples in which the liquid distribution has fully equilibrated. There was no signiﬁcant variation in the relationship between sample thickness and overall water content for drying under the varying conditions studied. This implies that for all conditions studied the retreat of the water distribution is due to the shrinkage of the cardboard sheet during drying rather than to the evolution of a receding evaporation front inside the sample. Up to a water content of 1.45 there is a linear relationship between sample thickness and the water content, however, there appears to be only a slight increase in the sample thickness between a water content of 1.45 and 2.0 (data not shown in Fig. 3.18). A linear ﬁt to the data for the calibration samples up to a water content of 1.45 gives a slope of 0.21 0.02 mm and an intercept of 0.61 0.02 mm, which compares well with the dry sample thickness of 0.56 0.03 mm determined by standard thickness measurement techniques. Figure 3.19 shows the temporal evolution of T1 and T2 relaxation times. As expected, both relaxation rates decrease with decreasing water concentration and show similar trends with water concentration, as observed for the calibration samples in Figure 3.15a and b. By summing across the proﬁles the total amount of water in the samples can be evaluated as a function of time and from this the drying rate can be calculated. Such

data are analogous to the drying kinetics as would be obtained, for example, by sample weighing. The effect of drying conditions on the drying kinetics is shown in Figs. 3.20 and 3.21. Figure 3.20 shows the variation in total water with time and Fig. 3.21 depicts the drying rate as a function of water mass per area in the sample. The drying rates increase with increasing temperature and air ﬂow rate and decrease with increasing

Fig. 3.20 Average total water mass per area as a function of drying time. Data are shown for drying conditions A (*), B (&), C (}), D (x), E ( þ ).

Fig. 3.21 Average drying rate against water mass per area during drying. Same legends as for Fig. 3.20.

humidity. For the 60 C experiments the cardboard is ﬁrst heated, which results in an initial increase in drying rate. The constant drying rates that can be calculated based on the difference in dry and wet bulb temperatures and the heat transfer coefﬁcient between air and cardboard are close to the maximum values presented in Fig. 3.21. Further insight into the drying process can be gained by studying the evolution of shape of the drying proﬁles over time. Analysis and comparison of the shapes of proﬁles under varying drying conditions is, however, complicated by several factors. First, due to sample variability the initial proﬁles show some variation in water content. The initial water content is not evenly distributed across the sample thickness but changes signiﬁcantly between the different sample layers. During the drying process the sample shrinks and so the physical position of a particular region of ﬁbers in the proﬁle changes. It is also possible that the sample develops a slight curvature during the drying process so that it is slightly misaligned at the end of drying. The overall rate of drying varies signiﬁcantly with the drying conditions so for a fair comparison of the shape of the proﬁle the different time scales involved must be compensated for. Some of these issues are to a large extent unavoidable. However, efforts were undertaken to compensate for the initial distribution of water concentration, the sample shrinkage and the varying time scales of drying. First, attempts were made to convert the distance scale to the cardboard frame of reference. This was achieved by deﬁning the length of the proﬁle as the region of the proﬁle with intensity greater than 40% of the maximum intensity and then re-scaling each proﬁle so that the proﬁle covered the same number of points, using a nearest neighbor interpolation method. To compensate for the initially uneven distribution of water in the

sample, all proﬁles were divided by the initial proﬁle acquired prior to the start of drying. Finally, to compensate for the varying time scales of the drying process the temporal evolution at each position was re-scaled to give the same number of proﬁles up to the point when the overall drying rate fell below 0.02 g m2 s1. Typical results of this analysis are shown in Fig. 3.22 for the experiments with the fastest overall drying rate (run A) and the slowest drying rate (run E), respectively. The proﬁles for the fastest drying rate show the development of a clear gradient as drying progresses, indicating that proportionally more water is lost from the outer layers of the cardboard than from the inner layer. This can be compared with drying at the slowest drying rate where the normalized proﬁle remains much ﬂatter during the drying process. At small drying rates water loss appears to be more uniform over the entire thickness of the cardboard. 3.3.3.5 Diffusion Measurements Further insight into the self-diffusivity of water and the mean pore sizes of the considered materials can be achieved with the so-called pulsed gradient spin–echo (PGSE) techniques. Such measurements were performed for the cardboard samples with the equipment as before. PGSE NMR measurements were conducted on the calibration samples and the original wetted sample. A stack of 5 cardboard samples approximately 5 mm by 30 mm was wrapped in plastic ﬁlm and placed vertically in a sealed 8 mm NMR tube. An initial horizontal 2D cross-sectional image of the cardboard stack was acquired to determine the orientation of the thickness direction. The stimulated echo PGSE scheme developed by Stejskal and Tanner (1965) was used in the diffusion measurements. The diffusion was measured over a time interval D, which was varied between 15 and 100 ms, and the diffusion gradient duration d was 2 ms. For each value of D studied, the gradient strength was varied in 32 even increments up to a maximal value of 194 Tcm1. Experiments were carried out with the diffusion gradient applied either parallel or perpendicular to the thickness direction. In addition to the

measurements on bulk samples, a set of diffusion weighted proﬁles was acquired for several calibration samples using the experimental set-up designed for the drying and calibration experiments. These experiments were used to test the similarity of the diffusion characteristics of the different layers in the composite sample. The diffusion weighted proﬁles showed no variation in the rate of signal intensity decay with increasing diffusion gradient strength across the sample thickness. This indicates that the three layers in the composite sample display similar diffusion behavior. The signal to noise ratio of these proﬁles was considerably poorer than in measurements on bulk samples due to the smaller sample size and extended T2 weighting involved in the diffusion proﬁling technique. For this reason, more detailed evaluation of the PGSE results was restricted to analysis of bulk, spatially unresolved measurements. Figure 3.23 shows typical signal intensity attenuation measured in the PGSE experiment for varying values of the observation time, D. If the water within the cardboard is characterized by a single self-diffusion coefﬁcient and the motion is not limited by any boundaries a plot of the logarithm of signal intensity log(S) against g2G2d2(D d/3), where g is the gyromagnetic ratio for protons, should be a straight line, the slope of which would give the diffusion coefﬁcient D, by ﬁtting to the relationship (Stejskal and Tanner, 1965) S d ¼ exp D g2 G2 d2 D Sð0Þ 3

ð3:16Þ

It can be seen in Fig. 3.23 that such a plot does not give a straight line and there is signiﬁcant variation in the signal attenuation with varying D. The water within the cellulose ﬁbers does not behave as a bulk liquid. Such curved log attenuation plots are

Fig. 3.23 Results from the PGSE experiments for cardboard with a water content of 1.45. Data are shown for D times of 15 (o), 30 (&), 50 (}), 75 (x) and 100 ( þ ) ms.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

usually indicative of either multiple diffusion regimes in the system, the diffusing species experiencing boundaries to their motion over the time scale of the diffusion measurement, or anisotropic diffusion, where the molecule motion is restricted to one or two dimensions. Pore sizes within the ﬁbers have been estimated by Scallan (1987), from solute exclusion techniques, to be in the range 2–20 nm. The molecular mean displacement hr(t)2i over time due to diffusion is given by the Einstein relation hr(t)2i ¼ 6Dt. The molecular mean displacement over the observation time D is much greater than the pore size. A water molecule would, consequently, move through several hundred pores even at the lowest water contents studied. The restriction caused by such pores would, thus, not lead to an observation time dependent diffusion coefﬁcient – but rather to a decrease in diffusion coefﬁcient compared to the free liquid. A model was therefore sought that results in a diffusion coefﬁcient that is independent of the observation time. For this reason, models such as the two-component diffusion model proposed by Li et al. (1992) to rationalize PGSE results of water in cellulose ﬁbers with higher moisture content than that used in the present study were not thought to be physically appropriate. Addams and Gladden (1999) interpreted PGSE results of water sorbed in cotton ﬁbers by means of a two-component exchange model. This two-component exchange model accounts directly for the changing shape of the attenuation plot with changing observation time, D, without having to assume an observation time dependence of the diffusion coefﬁcient. The two-component exchange model assumes the existence of two diffusion regimes and allows for exchange of molecules between the two environments during the observation time. The signal attenuation between the two phases is described by the relationships S d d 0 0 2 2 2 0 0 2 2 2 þ ð1p 2 Þexp D 2 g G d D ¼ p 1 exp D 1 g G d D S0 3 3 ð3:17Þ 9 8 1 1 1 > > > > D1 þ D2 þ 2 2 2 þ > > > > g d G t1 t2 > > < = 1 0 0 1 D 2; D 1 ¼ " # 2 > 2> > 2> > > 1 1 1 4 > > > > D þ þ þ D 2 1 ; : g2 d2 G2 t1 t2 g4 d4 G4 t 1 t 2 ð3:18Þ p02 ¼

according to K€arger et al. (1981) and Callaghan (1991). D1 and D2 are the diffusion coefﬁcients, t 1 and t 2 are the mean life times of molecules, and p1 and p2 are the relative populations in the two regions, respectively. Equation 3.17 was ﬁtted simultaneously to all the data acquired on each sample at different observation times, D. The ﬁt of the data to Eq. 3.17 is shown with solid lines in Fig. 3.23. The coefﬁcient of determination R2 for the ﬁts for all water contents studied was between 0.992 and 0.9999. The component corresponding to the region with faster diffusion was found to account for typically over 95% of the total water content of the system. The diffusion coefﬁcient of the major component, measured across the paper thickness has a value of 0.45 109 m2 s1 at a water content of 1.45 falling to 0.038 109 m2 s1 at a water content of 0.2. The decrease in this diffusion coefﬁcient with the water content in the sample is shown in Fig. 3.24 and indicates the shrinkage of pores in the ﬁbers with decreasing saturation. The diffusion coefﬁcient of the major component was found to be larger when measured parallel to the surface of the cardboard compared to when the measure-

Fig. 3.24 Fit of the diffusion coefficient of the major component for the PGSE experimental data to the two-component exchange model given by Eqs. 3.17–3.22; along the thickness direction (o) and perpendicular to the thickness direction (.) of the sample.

3.3 MRI Applications to Drying of Paper, Pulp and Wood Samples

ments were made across the thickness of the sample. This can, again, be explained by considering that the pores within the ﬁbers are elongated along the ﬁber axis, providing, on average, less hindrance to diffusion than across the ﬁber. The value of the diffusion coefﬁcient corresponding to the minor water fraction averaged over all water contents studied was 0.014 109 m2 s1, which is consistently over one order of magnitude smaller than the coefﬁcient of fast diffusion. This low diffusion coefﬁcient, as well as the fractional populations of the two components and the mean life time of molecules in the two components, showed no signiﬁcant or systematic variation with water content or direction of diffusion measurements. The average values of the mean life times for the major and minor components were 1.1 and 0.04 s, respectively, and the relative populations were on average 0.97 and 0.03, respectively. A physical interpretation of the results of this model could be that the bulk of the water in the ﬁber can be characterized by a single diffusion coefﬁcient which is independent of the observation time, while it is in exchange with a small fraction of the total water that has a much smaller diffusion coefﬁcient. This water could, for example, be the moisture sometimes described as non-freezing or, perhaps, water absorbed in the amorphous regions of the cellulose ﬁbers. Knowledge of the diffusion coefﬁcient of water within the ﬁbers and, in particular, of the concentration dependence of this diffusion coefﬁcient is useful for modeling studies and can also help to determine rate limiting steps for the drying process. It is instructive to compare the diffusion coefﬁcients measured by the PGSE technique with the effective liquid diffusivities used for modeling moisture transport through the porous cellulose network. Li et al. (1992) reported data for the self-diffusivity in pulp samples with moisture contents between 4.5 and 7. The diffusivity for the bulk water between the ﬁbers was in the range 1.12–1.47 109 m2 s1 and the diffusivity for the restricted water in the oderman (2002) pores was between 0.14 and 0.49 109 m2 s1. Topgaard and S€ communicated values ranging from 4 1011 m2 s1 at a moisture content of 0.1 to 0.9 109 m2 s1 at a moisture content of 0.7. At this moisture content it can be assumed that most of the water is within the intra-ﬁber pores. All the experimental self-diffusivities presented above are below the self-diffusivity for free water at 25 C, which was given by Topgaard (2003) to be 2.3 109 m2 s1. At high moisture loads the difference is a factor of 2 while at low moisture content the difference is a factor of about 50. The liquid self-diffusivities measured by Topgaard and S€ oderman (2002) were used in a modeling study by Baggerud (2004) to calculate the moisture and temperature gradients in a number of paper and pulp samples. Mass transfer could occur both by gas phase and liquid diffusion through the porous materials. The liquid diffusivity was calculated according to 8 3:7 >